Practice sheet

Fresh questions from the whole chapter, to do on paper.

New questions Include answers

To save a PDF, choose “Save as PDF” in the print dialog.

Many random samples of size 161 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 224 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 490 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 260 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 439 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 410 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 315 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 242 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 409 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 473 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 423 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 230 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 173 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 198 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 58 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 467 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 96 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 195 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 81 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 334 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 91 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 124 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 367 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 487 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 238 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 351 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 113 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 189 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 391 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 382 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 319 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 52 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 220 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 51 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 337 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 316 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 393 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 452 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 102 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 62 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 208 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 95 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 450 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 443 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 75 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 477 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 286 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 374 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 428 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Many random samples of size 66 are taken from the same population. Which quantity changes from sample to sample?
1. The sample proportion p̂ (a statistic)
2. The population proportion p (a parameter)
3. The sample size
Compared with samples of size 73, samples of size 292 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 72, samples of size 288 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 32, samples of size 128 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 41, samples of size 164 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 127, samples of size 508 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 193, samples of size 772 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 25, samples of size 100 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 80, samples of size 320 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 197, samples of size 788 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 97, samples of size 388 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 66, samples of size 264 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 151, samples of size 604 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 113, samples of size 452 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 84, samples of size 336 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 192, samples of size 768 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 104, samples of size 416 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 107, samples of size 428 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 147, samples of size 588 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 155, samples of size 620 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 116, samples of size 464 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 67, samples of size 268 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 60, samples of size 240 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 137, samples of size 548 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 55, samples of size 220 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 23, samples of size 92 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 65, samples of size 260 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 77, samples of size 308 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 45, samples of size 180 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 93, samples of size 372 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 74, samples of size 296 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 46, samples of size 184 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 159, samples of size 636 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 30, samples of size 120 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 21, samples of size 84 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 191, samples of size 764 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 182, samples of size 728 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 123, samples of size 492 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 153, samples of size 612 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 114, samples of size 456 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 90, samples of size 360 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 117, samples of size 468 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 198, samples of size 792 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 63, samples of size 252 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 102, samples of size 408 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 98, samples of size 392 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 82, samples of size 328 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 89, samples of size 356 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 119, samples of size 476 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 174, samples of size 696 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
Compared with samples of size 190, samples of size 760 give sample means that…
1. vary less around the population mean
2. vary more
3. are more biased
What is the sampling distribution of the sample mean for samples of size 25?
1. The distribution of x̄ over all possible samples of size 25
2. The distribution of the 25 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 23?
1. The distribution of x̄ over all possible samples of size 23
2. The distribution of the 23 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 46?
1. The distribution of x̄ over all possible samples of size 46
2. The distribution of the 46 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 40?
1. The distribution of x̄ over all possible samples of size 40
2. The distribution of the 40 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 38?
1. The distribution of x̄ over all possible samples of size 38
2. The distribution of the 38 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 86?
1. The distribution of x̄ over all possible samples of size 86
2. The distribution of the 86 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 152?
1. The distribution of x̄ over all possible samples of size 152
2. The distribution of the 152 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 72?
1. The distribution of x̄ over all possible samples of size 72
2. The distribution of the 72 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 159?
1. The distribution of x̄ over all possible samples of size 159
2. The distribution of the 159 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 98?
1. The distribution of x̄ over all possible samples of size 98
2. The distribution of the 98 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 91?
1. The distribution of x̄ over all possible samples of size 91
2. The distribution of the 91 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 59?
1. The distribution of x̄ over all possible samples of size 59
2. The distribution of the 59 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 22?
1. The distribution of x̄ over all possible samples of size 22
2. The distribution of the 22 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 80?
1. The distribution of x̄ over all possible samples of size 80
2. The distribution of the 80 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 162?
1. The distribution of x̄ over all possible samples of size 162
2. The distribution of the 162 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 55?
1. The distribution of x̄ over all possible samples of size 55
2. The distribution of the 55 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 37?
1. The distribution of x̄ over all possible samples of size 37
2. The distribution of the 37 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 56?
1. The distribution of x̄ over all possible samples of size 56
2. The distribution of the 56 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 160?
1. The distribution of x̄ over all possible samples of size 160
2. The distribution of the 160 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 130?
1. The distribution of x̄ over all possible samples of size 130
2. The distribution of the 130 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 67?
1. The distribution of x̄ over all possible samples of size 67
2. The distribution of the 67 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 28?
1. The distribution of x̄ over all possible samples of size 28
2. The distribution of the 28 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 173?
1. The distribution of x̄ over all possible samples of size 173
2. The distribution of the 173 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 69?
1. The distribution of x̄ over all possible samples of size 69
2. The distribution of the 69 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 153?
1. The distribution of x̄ over all possible samples of size 153
2. The distribution of the 153 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 199?
1. The distribution of x̄ over all possible samples of size 199
2. The distribution of the 199 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 106?
1. The distribution of x̄ over all possible samples of size 106
2. The distribution of the 106 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 104?
1. The distribution of x̄ over all possible samples of size 104
2. The distribution of the 104 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 184?
1. The distribution of x̄ over all possible samples of size 184
2. The distribution of the 184 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 133?
1. The distribution of x̄ over all possible samples of size 133
2. The distribution of the 133 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 21?
1. The distribution of x̄ over all possible samples of size 21
2. The distribution of the 21 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 93?
1. The distribution of x̄ over all possible samples of size 93
2. The distribution of the 93 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 167?
1. The distribution of x̄ over all possible samples of size 167
2. The distribution of the 167 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 97?
1. The distribution of x̄ over all possible samples of size 97
2. The distribution of the 97 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 48?
1. The distribution of x̄ over all possible samples of size 48
2. The distribution of the 48 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 61?
1. The distribution of x̄ over all possible samples of size 61
2. The distribution of the 61 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 32?
1. The distribution of x̄ over all possible samples of size 32
2. The distribution of the 32 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 166?
1. The distribution of x̄ over all possible samples of size 166
2. The distribution of the 166 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 176?
1. The distribution of x̄ over all possible samples of size 176
2. The distribution of the 176 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 62?
1. The distribution of x̄ over all possible samples of size 62
2. The distribution of the 62 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 195?
1. The distribution of x̄ over all possible samples of size 195
2. The distribution of the 195 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 95?
1. The distribution of x̄ over all possible samples of size 95
2. The distribution of the 95 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 121?
1. The distribution of x̄ over all possible samples of size 121
2. The distribution of the 121 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 123?
1. The distribution of x̄ over all possible samples of size 123
2. The distribution of the 123 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 83?
1. The distribution of x̄ over all possible samples of size 83
2. The distribution of the 83 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 45?
1. The distribution of x̄ over all possible samples of size 45
2. The distribution of the 45 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 124?
1. The distribution of x̄ over all possible samples of size 124
2. The distribution of the 124 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 113?
1. The distribution of x̄ over all possible samples of size 113
2. The distribution of the 113 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 35?
1. The distribution of x̄ over all possible samples of size 35
2. The distribution of the 35 values in one sample
3. The distribution of the population
What is the sampling distribution of the sample mean for samples of size 65?
1. The distribution of x̄ over all possible samples of size 65
2. The distribution of the 65 values in one sample
3. The distribution of the population
The population proportion is p = 8/10. Find the standard deviation of p̂ for random samples of size 83.
The population proportion is p = 5/10. What is the mean of the sampling distribution of p̂ for samples of size 351?
The population proportion is p = 1/8. What is the smallest sample size n for which np ≥ 10 and n(1 − p) ≥ 10?
A population has standard deviation σ = 9. Find the SD of the sample mean for samples of size 49.
Samples of size 26 give a certain SD of x̄. By what factor must the sample size be multiplied to halve it?
A population has mean 76 and SD 5. A random sample of 4 has mean 77. Find the z-score of this sample mean.
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 52 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 73 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 72 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 65 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 83 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 43 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 54 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 70 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 88 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 53 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 95 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 63 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 61 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 92 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 97 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 56 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 64 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 50 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 77 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 69 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 74 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 60 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 47 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 62 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 76 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 93 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 40 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 99 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 49 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 79 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 84 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 42 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 46 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 82 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 57 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 41 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 59 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 100 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 71 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 75 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 81 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 45 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 66 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 58 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 98 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 80 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 96 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 89 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 68 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
Household incomes are strongly right-skewed. What is the shape of the sampling distribution of x̄ for random samples of 86 households?
1. Approximately normal, by the central limit theorem
2. Right-skewed like the population
3. Uniform
A population is strongly skewed. Is the sampling distribution of x̄ for samples of size 3 approximately normal?
1. Not necessarily: n = 3 is too small for the CLT to apply to a strongly skewed population
2. Yes, sample means are always normal
3. No, sample means are never normal
A population is strongly skewed. Is the sampling distribution of x̄ for samples of size 5 approximately normal?
1. Not necessarily: n = 5 is too small for the CLT to apply to a strongly skewed population
2. Yes, sample means are always normal
3. No, sample means are never normal
A population is strongly skewed. Is the sampling distribution of x̄ for samples of size 6 approximately normal?
1. Not necessarily: n = 6 is too small for the CLT to apply to a strongly skewed population
2. Yes, sample means are always normal
3. No, sample means are never normal
A population is strongly skewed. Is the sampling distribution of x̄ for samples of size 4 approximately normal?
1. Not necessarily: n = 4 is too small for the CLT to apply to a strongly skewed population
2. Yes, sample means are always normal
3. No, sample means are never normal
Which statement is the central limit theorem, for random samples of size 166?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 107?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 99?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 90?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 136?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 200?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 102?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 80?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 121?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 193?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 132?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 101?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 133?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 154?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 157?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 113?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 198?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 140?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 69?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 54?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 48?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 78?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 86?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 96?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 98?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 114?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 45?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 156?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 70?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 75?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 197?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 134?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 153?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 46?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 73?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 199?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 71?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 141?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 152?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 47?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 172?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 169?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 185?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 123?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 184?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 161?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 94?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 60?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 66?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Which statement is the central limit theorem, for random samples of size 76?
1. The distribution of sample means is approximately normal
2. The data in a large sample are approximately normal
3. The population becomes normal when n is large
Independent random samples of 100 are taken from two populations with proportions 8/10 and 1/10. Find the SD of p̂₁ − p̂₂.
Independent samples of size 4 come from populations with SDs 36 and 48. Find the SD of x̄₁ − x̄₂.
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 66)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 130)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 53)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 160)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 169)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 145)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 140)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 139)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 45)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 171)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 59)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 99)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 114)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 92)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 64)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 27)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 94)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 33)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 60)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 105)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 83)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 162)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 146)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 198)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 65)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 55)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 127)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 76)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 74)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 81)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 187)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 121)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 90)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 135)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 141)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 50)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 30)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 88)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 57)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 115)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 47)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 138)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 46)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 21)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 199)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 131)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 84)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 111)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 93)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
When are the variances of x̄₁ and x̄₂ added to get the variance of x̄₁ − x̄₂ (samples of 58)?
1. When the two samples are independent
2. Only when the sample sizes are equal
3. Always, even for paired measurements
What does it mean that p̂ is an unbiased estimator of p (samples of 40)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 187)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 106)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 92)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 33)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 74)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 48)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 104)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 130)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 125)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 58)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 153)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 117)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 42)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 172)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 87)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 63)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 98)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 111)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 179)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 73)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 82)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 39)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 60)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 132)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 41)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 200)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 119)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 52)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 105)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 69)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 22)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 178)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 24)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 78)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 142)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 85)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 154)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 55)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 25)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 158)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 43)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 45)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 90)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 38)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 62)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 75)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 28)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 180)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
What does it mean that p̂ is an unbiased estimator of p (samples of 148)?
1. The mean of its sampling distribution equals p
2. Every sample gives p̂ = p
3. Its variability is small
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 116)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 126)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 46)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 192)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 115)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 179)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 99)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 44)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 190)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 85)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 112)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 98)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 195)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 97)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 24)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 196)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 174)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 177)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 111)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 165)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 27)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 52)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 26)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 29)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 145)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 65)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 170)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 118)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 155)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 127)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 158)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 137)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 162)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 50)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 80)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 188)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 198)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 94)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 22)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 42)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 183)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 169)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 197)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 48)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 157)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 23)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 72)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 150)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 31)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A survey method gives estimates that cluster tightly, but far from the true value. How would you describe it (samples of 70)?
1. Biased, with low variability
2. Unbiased, with low variability
3. Unbiased, with high variability
A school has 1200 students. Sampling without replacement, what is the largest sample size that meets the 10% condition?

Answers

The sample proportion p̂ (a statistic)
vary less around the population mean
The distribution of x̄ over all possible samples of size 25
$\frac{2 \sqrt{83}}{415}$
$\frac{1}{2}$
$80$
$\frac{9}{7}$
$4$
$\frac{2}{5}$
Approximately normal, by the central limit theorem
Not necessarily: n = 3 is too small for the CLT to apply to a strongly skewed population
The distribution of sample means is approximately normal
$\frac{1}{20}$
$30$
When the two samples are independent
The mean of its sampling distribution equals p
Biased, with low variability
$120$