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.

A company claims that 80% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.80
2. H₀: p < 0.80
3. H₀: p̂ = 0.80
A company claims that 60% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.60
2. H₀: p < 0.60
3. H₀: p̂ = 0.60
A company claims that 62% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.62
2. H₀: p < 0.62
3. H₀: p̂ = 0.62
A company claims that 29% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.29
2. H₀: p < 0.29
3. H₀: p̂ = 0.29
A company claims that 48% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.48
2. H₀: p < 0.48
3. H₀: p̂ = 0.48
A company claims that 71% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.71
2. H₀: p < 0.71
3. H₀: p̂ = 0.71
A company claims that 59% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.59
2. H₀: p < 0.59
3. H₀: p̂ = 0.59
A company claims that 73% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.73
2. H₀: p < 0.73
3. H₀: p̂ = 0.73
A company claims that 66% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.66
2. H₀: p < 0.66
3. H₀: p̂ = 0.66
A company claims that 26% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.26
2. H₀: p < 0.26
3. H₀: p̂ = 0.26
A company claims that 22% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.22
2. H₀: p < 0.22
3. H₀: p̂ = 0.22
A company claims that 27% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.27
2. H₀: p < 0.27
3. H₀: p̂ = 0.27
A company claims that 23% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.23
2. H₀: p < 0.23
3. H₀: p̂ = 0.23
A company claims that 58% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.58
2. H₀: p < 0.58
3. H₀: p̂ = 0.58
A company claims that 28% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.28
2. H₀: p < 0.28
3. H₀: p̂ = 0.28
A company claims that 61% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.61
2. H₀: p < 0.61
3. H₀: p̂ = 0.61
A company claims that 50% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.50
2. H₀: p < 0.50
3. H₀: p̂ = 0.50
A company claims that 43% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.43
2. H₀: p < 0.43
3. H₀: p̂ = 0.43
A company claims that 52% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.52
2. H₀: p < 0.52
3. H₀: p̂ = 0.52
A company claims that 44% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.44
2. H₀: p < 0.44
3. H₀: p̂ = 0.44
A company claims that 65% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.65
2. H₀: p < 0.65
3. H₀: p̂ = 0.65
A company claims that 70% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.70
2. H₀: p < 0.70
3. H₀: p̂ = 0.70
A company claims that 72% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.72
2. H₀: p < 0.72
3. H₀: p̂ = 0.72
A company claims that 63% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.63
2. H₀: p < 0.63
3. H₀: p̂ = 0.63
A company claims that 49% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.49
2. H₀: p < 0.49
3. H₀: p̂ = 0.49
A company claims that 31% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.31
2. H₀: p < 0.31
3. H₀: p̂ = 0.31
A company claims that 56% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.56
2. H₀: p < 0.56
3. H₀: p̂ = 0.56
A company claims that 33% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.33
2. H₀: p < 0.33
3. H₀: p̂ = 0.33
A company claims that 68% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.68
2. H₀: p < 0.68
3. H₀: p̂ = 0.68
A company claims that 21% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.21
2. H₀: p < 0.21
3. H₀: p̂ = 0.21
A company claims that 51% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.51
2. H₀: p < 0.51
3. H₀: p̂ = 0.51
A company claims that 64% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.64
2. H₀: p < 0.64
3. H₀: p̂ = 0.64
A company claims that 24% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.24
2. H₀: p < 0.24
3. H₀: p̂ = 0.24
A company claims that 67% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.67
2. H₀: p < 0.67
3. H₀: p̂ = 0.67
A company claims that 36% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.36
2. H₀: p < 0.36
3. H₀: p̂ = 0.36
A company claims that 25% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.25
2. H₀: p < 0.25
3. H₀: p̂ = 0.25
A company claims that 32% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.32
2. H₀: p < 0.32
3. H₀: p̂ = 0.32
A company claims that 55% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.55
2. H₀: p < 0.55
3. H₀: p̂ = 0.55
A company claims that 53% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.53
2. H₀: p < 0.53
3. H₀: p̂ = 0.53
A company claims that 38% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.38
2. H₀: p < 0.38
3. H₀: p̂ = 0.38
A company claims that 69% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.69
2. H₀: p < 0.69
3. H₀: p̂ = 0.69
A company claims that 74% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.74
2. H₀: p < 0.74
3. H₀: p̂ = 0.74
A company claims that 77% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.77
2. H₀: p < 0.77
3. H₀: p̂ = 0.77
A company claims that 79% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.79
2. H₀: p < 0.79
3. H₀: p̂ = 0.79
A company claims that 46% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.46
2. H₀: p < 0.46
3. H₀: p̂ = 0.46
A company claims that 30% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.30
2. H₀: p < 0.30
3. H₀: p̂ = 0.30
A company claims that 42% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.42
2. H₀: p < 0.42
3. H₀: p̂ = 0.42
A company claims that 37% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.37
2. H₀: p < 0.37
3. H₀: p̂ = 0.37
A company claims that 54% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.54
2. H₀: p < 0.54
3. H₀: p̂ = 0.54
A company claims that 75% of customers are satisfied. A researcher suspects fewer are. Which is the null hypothesis?
1. H₀: p = 0.75
2. H₀: p < 0.75
3. H₀: p̂ = 0.75
The mean wait at a clinic used to be 81 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 81
2. Hₐ: μ > 81
3. Hₐ: x̄ ≠ 81
The mean wait at a clinic used to be 53 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 53
2. Hₐ: μ > 53
3. Hₐ: x̄ ≠ 53
The mean wait at a clinic used to be 37 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 37
2. Hₐ: μ > 37
3. Hₐ: x̄ ≠ 37
The mean wait at a clinic used to be 21 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 21
2. Hₐ: μ > 21
3. Hₐ: x̄ ≠ 21
The mean wait at a clinic used to be 69 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 69
2. Hₐ: μ > 69
3. Hₐ: x̄ ≠ 69
The mean wait at a clinic used to be 85 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 85
2. Hₐ: μ > 85
3. Hₐ: x̄ ≠ 85
The mean wait at a clinic used to be 25 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 25
2. Hₐ: μ > 25
3. Hₐ: x̄ ≠ 25
The mean wait at a clinic used to be 88 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 88
2. Hₐ: μ > 88
3. Hₐ: x̄ ≠ 88
The mean wait at a clinic used to be 67 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 67
2. Hₐ: μ > 67
3. Hₐ: x̄ ≠ 67
The mean wait at a clinic used to be 57 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 57
2. Hₐ: μ > 57
3. Hₐ: x̄ ≠ 57
The mean wait at a clinic used to be 24 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 24
2. Hₐ: μ > 24
3. Hₐ: x̄ ≠ 24
The mean wait at a clinic used to be 82 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 82
2. Hₐ: μ > 82
3. Hₐ: x̄ ≠ 82
The mean wait at a clinic used to be 23 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 23
2. Hₐ: μ > 23
3. Hₐ: x̄ ≠ 23
The mean wait at a clinic used to be 55 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 55
2. Hₐ: μ > 55
3. Hₐ: x̄ ≠ 55
The mean wait at a clinic used to be 90 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 90
2. Hₐ: μ > 90
3. Hₐ: x̄ ≠ 90
The mean wait at a clinic used to be 80 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 80
2. Hₐ: μ > 80
3. Hₐ: x̄ ≠ 80
The mean wait at a clinic used to be 26 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 26
2. Hₐ: μ > 26
3. Hₐ: x̄ ≠ 26
The mean wait at a clinic used to be 79 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 79
2. Hₐ: μ > 79
3. Hₐ: x̄ ≠ 79
The mean wait at a clinic used to be 22 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 22
2. Hₐ: μ > 22
3. Hₐ: x̄ ≠ 22
The mean wait at a clinic used to be 33 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 33
2. Hₐ: μ > 33
3. Hₐ: x̄ ≠ 33
The mean wait at a clinic used to be 29 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 29
2. Hₐ: μ > 29
3. Hₐ: x̄ ≠ 29
The mean wait at a clinic used to be 70 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 70
2. Hₐ: μ > 70
3. Hₐ: x̄ ≠ 70
The mean wait at a clinic used to be 47 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 47
2. Hₐ: μ > 47
3. Hₐ: x̄ ≠ 47
The mean wait at a clinic used to be 76 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 76
2. Hₐ: μ > 76
3. Hₐ: x̄ ≠ 76
The mean wait at a clinic used to be 61 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 61
2. Hₐ: μ > 61
3. Hₐ: x̄ ≠ 61
The mean wait at a clinic used to be 87 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 87
2. Hₐ: μ > 87
3. Hₐ: x̄ ≠ 87
The mean wait at a clinic used to be 54 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 54
2. Hₐ: μ > 54
3. Hₐ: x̄ ≠ 54
The mean wait at a clinic used to be 38 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 38
2. Hₐ: μ > 38
3. Hₐ: x̄ ≠ 38
The mean wait at a clinic used to be 58 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 58
2. Hₐ: μ > 58
3. Hₐ: x̄ ≠ 58
The mean wait at a clinic used to be 65 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 65
2. Hₐ: μ > 65
3. Hₐ: x̄ ≠ 65
The mean wait at a clinic used to be 74 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 74
2. Hₐ: μ > 74
3. Hₐ: x̄ ≠ 74
The mean wait at a clinic used to be 30 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 30
2. Hₐ: μ > 30
3. Hₐ: x̄ ≠ 30
The mean wait at a clinic used to be 44 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 44
2. Hₐ: μ > 44
3. Hₐ: x̄ ≠ 44
The mean wait at a clinic used to be 72 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 72
2. Hₐ: μ > 72
3. Hₐ: x̄ ≠ 72
The mean wait at a clinic used to be 75 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 75
2. Hₐ: μ > 75
3. Hₐ: x̄ ≠ 75
The mean wait at a clinic used to be 36 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 36
2. Hₐ: μ > 36
3. Hₐ: x̄ ≠ 36
The mean wait at a clinic used to be 64 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 64
2. Hₐ: μ > 64
3. Hₐ: x̄ ≠ 64
The mean wait at a clinic used to be 56 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 56
2. Hₐ: μ > 56
3. Hₐ: x̄ ≠ 56
The mean wait at a clinic used to be 60 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 60
2. Hₐ: μ > 60
3. Hₐ: x̄ ≠ 60
The mean wait at a clinic used to be 89 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 89
2. Hₐ: μ > 89
3. Hₐ: x̄ ≠ 89
The mean wait at a clinic used to be 39 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 39
2. Hₐ: μ > 39
3. Hₐ: x̄ ≠ 39
The mean wait at a clinic used to be 32 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 32
2. Hₐ: μ > 32
3. Hₐ: x̄ ≠ 32
The mean wait at a clinic used to be 40 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 40
2. Hₐ: μ > 40
3. Hₐ: x̄ ≠ 40
The mean wait at a clinic used to be 43 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 43
2. Hₐ: μ > 43
3. Hₐ: x̄ ≠ 43
The mean wait at a clinic used to be 48 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 48
2. Hₐ: μ > 48
3. Hₐ: x̄ ≠ 48
The mean wait at a clinic used to be 41 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 41
2. Hₐ: μ > 41
3. Hₐ: x̄ ≠ 41
The mean wait at a clinic used to be 84 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 84
2. Hₐ: μ > 84
3. Hₐ: x̄ ≠ 84
The mean wait at a clinic used to be 86 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 86
2. Hₐ: μ > 86
3. Hₐ: x̄ ≠ 86
The mean wait at a clinic used to be 46 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 46
2. Hₐ: μ > 46
3. Hₐ: x̄ ≠ 46
The mean wait at a clinic used to be 71 minutes. A manager wants to know whether it has changed, in either direction. Which alternative?
1. Hₐ: μ ≠ 71
2. Hₐ: μ > 71
3. Hₐ: x̄ ≠ 71
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 445)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 385)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 159)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 479)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 194)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 244)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 425)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 325)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 264)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 315)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 73)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 444)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 450)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 65)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 303)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 408)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 352)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 157)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 50)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 368)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 181)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 263)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 156)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 139)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 213)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 54)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 147)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 340)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 220)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 52)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 496)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 155)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 317)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 324)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 378)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 491)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 69)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 251)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 414)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 253)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 478)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 422)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 439)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 74)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 178)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 282)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 95)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 483)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 266)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Why are hypotheses written about parameters such as p, not statistics such as p̂ (sample of 242)?
1. Because we know p̂ exactly; the question is about the unknown population value
2. Because statistics are harder to compute
3. There is no difference between p and p̂
Test H₀: p = 0.5 with a random sample of 100 in which p̂ = 52/100. Find the z statistic.
Test H₀: p = 0.2 with n = 400 and p̂ = 28/100. Find the z statistic.
A test gives a P-value of 0.05. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.05
2. There is a 0.05 probability that H₀ is true
3. The result is due to chance with probability 0.05
A test gives a P-value of 0.09. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.09
2. There is a 0.09 probability that H₀ is true
3. The result is due to chance with probability 0.09
A test gives a P-value of 0.02. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.02
2. There is a 0.02 probability that H₀ is true
3. The result is due to chance with probability 0.02
A test gives a P-value of 0.03. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.03
2. There is a 0.03 probability that H₀ is true
3. The result is due to chance with probability 0.03
A test gives a P-value of 0.06. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.06
2. There is a 0.06 probability that H₀ is true
3. The result is due to chance with probability 0.06
A test gives a P-value of 0.07. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.07
2. There is a 0.07 probability that H₀ is true
3. The result is due to chance with probability 0.07
A test gives a P-value of 0.08. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.08
2. There is a 0.08 probability that H₀ is true
3. The result is due to chance with probability 0.08
A test gives a P-value of 0.04. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.04
2. There is a 0.04 probability that H₀ is true
3. The result is due to chance with probability 0.04
A test gives a P-value of 0.01. What does it mean?
1. If H₀ were true, a result at least as extreme as ours would happen with probability 0.01
2. There is a 0.01 probability that H₀ is true
3. The result is due to chance with probability 0.01
At significance level α = 0.05, a test gives P-value 0.04. What do you conclude?
1. Reject H₀: there is convincing evidence for Hₐ
2. Accept H₀
3. Hₐ is proven true
At significance level α = 0.05, a test gives P-value 0.03. What do you conclude?
1. Reject H₀: there is convincing evidence for Hₐ
2. Accept H₀
3. Hₐ is proven true
At significance level α = 0.05, a test gives P-value 0.02. What do you conclude?
1. Reject H₀: there is convincing evidence for Hₐ
2. Accept H₀
3. Hₐ is proven true
At significance level α = 0.05, a test gives P-value 0.01. What do you conclude?
1. Reject H₀: there is convincing evidence for Hₐ
2. Accept H₀
3. Hₐ is proven true
A test of a new drug (sample of 388) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 333) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 94) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 210) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 498) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 450) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 259) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 187) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 393) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 292) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 198) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 350) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 61) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 497) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 269) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 122) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 179) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 135) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 339) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 361) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 431) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 421) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 171) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 185) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 108) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 272) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 237) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 320) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 381) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 316) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 317) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 60) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 197) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 414) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 262) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 438) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 177) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 188) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 139) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 115) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 157) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 436) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 191) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 471) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 104) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 287) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 134) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 330) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 221) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
A test of a new drug (sample of 473) has H₀: the drug has no effect. What is a Type I error?
1. Concluding the drug works when it really has no effect
2. Concluding there is no effect when the drug really works
3. Making a mistake in the data
How can a researcher increase the power of a test that now uses 82 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 137 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 297 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 149 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 244 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 203 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 210 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 110 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 166 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 253 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 290 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 195 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 275 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 259 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 296 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 128 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 294 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 81 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 133 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 85 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 151 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 123 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 282 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 61 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 72 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 113 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 248 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 229 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 95 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 89 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 94 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 126 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 236 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 172 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 169 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 288 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 106 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 116 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 59 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 176 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 279 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 135 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 51 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 57 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 188 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 156 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 140 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 53 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 171 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
How can a researcher increase the power of a test that now uses 273 subjects?
1. Use a larger sample
2. Use a smaller α
3. Use fewer subjects
Test H₀: μ = 39. A random sample of 9 has x̄ = 43 and s = 9. Find the t statistic.
A t test gives P-value 0.20. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.50. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.28. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.45. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.57. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.58. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.10. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.44. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.26. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.30. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.31. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.32. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.55. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.39. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.42. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.53. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.49. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.40. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.60. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.11. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.54. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.23. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.59. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.17. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.22. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.38. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.43. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.25. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.19. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.21. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.13. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.27. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.48. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.41. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.18. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.15. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.29. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.12. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.46. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.14. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.36. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.24. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.34. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.16. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.47. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.56. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.37. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.51. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.33. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
A t test gives P-value 0.35. What can you conclude at α = 0.05?
1. Fail to reject H₀: not enough evidence for Hₐ
2. H₀ is true
3. Reject H₀
For a test statistic, the area in one tail beyond it is 0.04. Find the P-value of the two-sided test.
To test H₀: p₁ = p₂, group 1 had 21 successes out of 82 and group 2 had 22 out of 102. Find the pooled proportion.
24 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 24 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
10 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 10 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
38 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 38 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
13 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 13 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
17 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 17 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
31 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 31 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
14 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 14 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
18 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 18 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
39 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 39 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
20 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 20 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
25 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 25 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
37 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 37 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
34 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 34 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
22 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 22 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
16 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 16 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
27 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 27 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
11 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 11 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
29 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 29 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
23 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 23 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
12 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 12 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
35 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 35 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
33 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 33 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
19 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 19 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
28 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 28 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
30 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 30 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
32 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 32 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
21 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 21 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
40 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 40 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
26 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 26 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
15 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 15 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
36 students take a test before and after a course. Which procedure compares the scores?
1. A paired t test on the 36 differences (after − before)
2. A two-sample t test treating the groups as independent
3. A two-proportion z test
Testing H₀: p₁ = p₂ with n₁ = n₂ = 100, the pooled proportion is 3/10. Find the standard error of p̂₁ − p̂₂.
A die is rolled 114 times to test whether it is fair. What is the expected count for each face?
In a chi-square test, one category has observed count 39 and expected count 21. Find its contribution to χ².
In a two-way table with grand total 158, a row total is 55 and a column total is 41. Find the expected count in that cell under independence.

Answers

H₀: p = 0.80
Hₐ: μ ≠ 81
Because we know p̂ exactly; the question is about the unknown population value
$\frac{2}{5}$
$4$
If H₀ were true, a result at least as extreme as ours would happen with probability 0.05
Reject H₀: there is convincing evidence for Hₐ
Concluding the drug works when it really has no effect
Use a larger sample
$\frac{4}{3}$
Fail to reject H₀: not enough evidence for Hₐ
$\frac{2}{25}$
$\frac{43}{184}$
A paired t test on the 24 differences (after − before)
$\frac{\sqrt{42}}{100}$
$19$
$\frac{108}{7}$
$\frac{2255}{158}$