Inferences and conclusions from data

Practice sheet

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

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  1. A researcher measures the sleep of 376 randomly chosen teenagers and finds a mean of 7.1 hours. What is 7.1?
    1. A statistic: it describes the sample
    2. A parameter: it describes all teenagers
    3. The population
  2. To learn how much US college students spend on books, a team surveys 671 students at 20 colleges. What is the population?
    1. All US college students
    2. The 671 students surveyed
    3. The 20 colleges
  3. Census records show that 52% of all households in a town own a car. What is 52%?
    1. A parameter: it describes the whole population
    2. A statistic
    3. A sample proportion
  4. A news website asks readers to vote online; 4824 vote and 80% favor a new law. What is the main problem?
    1. Voluntary response bias: people with strong opinions choose to respond
    2. The sample is too small
    3. None: 4824 responses are representative
  5. A survey of 115 adults is done by calling landline numbers. What kind of bias is most likely?
    1. Undercoverage: people without landlines cannot be chosen
    2. Response bias from the wording
    3. None, if the numbers are chosen at random
  6. A biased survey of 238 people is repeated with 10 times as many people, chosen the same way. What happens to the bias?
    1. It stays: a larger sample reduces random variability, not bias
    2. It disappears
    3. It becomes 10 times smaller
  7. 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.
  8. 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
  9. Testing H₀: p₁ = p₂ with n₁ = n₂ = 100, the pooled proportion is 3/10. Find the standard error of p̂₁ − p̂₂.
  10. Test scores have mean 75 and standard deviation 3. Find the z-score of a score of 52.
  11. Heights are approximately normal with mean 76 and standard deviation 4. By the 68–95–99.7 rule, what percent are between 72 and 84?
  12. Mean 71, standard deviation 8. Which value has z-score −3-3?