AP Stats Stats: Evaluation Overview 2 — Questions and Answers
Question 1: A researcher wants to test whether a new drug reduces blood pressure. Which type of study provides the strongest evidence of causation?
- Observational cohort study
- Randomized controlled experiment (Correct answer)
- Stratified survey
- Case-control study
Correct answer: Randomized controlled experiment
Randomized controlled experiments allow causal conclusions because random assignment controls for confounding variables.
Question 2: In hypothesis testing, the p-value represents:
- The probability the null hypothesis is true
- The probability of observing results at least as extreme as the sample, assuming H₀ is true (Correct answer)
- The probability the alternative hypothesis is true
- The significance level chosen by the researcher
Correct answer: The probability of observing results at least as extreme as the sample, assuming H₀ is true
The p-value is the probability of obtaining a test statistic as extreme or more extreme than observed, given H₀ is true.
Question 3: A 95% confidence interval for a population mean is (12.4, 18.6). Which interpretation is correct?
- There is a 95% chance the true mean falls in this interval
- 95% of sample means fall between 12.4 and 18.6
- If we repeated sampling many times, about 95% of such intervals would contain the true mean (Correct answer)
- The sample mean has a 95% probability of being correct
Correct answer: If we repeated sampling many times, about 95% of such intervals would contain the true mean
Confidence level refers to the long-run proportion of intervals constructed this way that capture the true parameter.
Question 4: Which of the following is an example of a Type I error?
- Failing to reject a false null hypothesis
- Rejecting a true null hypothesis (Correct answer)
- Setting alpha too small
- Using a one-tailed test instead of two-tailed
Correct answer: Rejecting a true null hypothesis
A Type I error (false positive) occurs when we reject H₀ even though it is actually true.
Question 5: A scatterplot shows a strong negative linear association between two variables. The correlation coefficient r is most likely:
- 0.85
- 0.05
- -0.92 (Correct answer)
- -0.10
Correct answer: -0.92
A strong negative linear association corresponds to r close to -1, making -0.92 the best choice.
Question 6: Which condition must be checked when performing a chi-square test for independence?
- All expected cell counts are at least 5 (Correct answer)
- All observed cell counts are equal
- The sample size is less than 30
- The variables are normally distributed
Correct answer: All expected cell counts are at least 5
The chi-square approximation is valid only when all expected cell frequencies are at least 5.
Question 7: A school surveys a random sample of 200 students and finds 60% prefer online learning. The margin of error at 95% confidence is ±6.8%. What does this margin of error indicate?
- 60% of the population prefers online learning
- The true proportion is exactly between 53.2% and 66.8%
- We are 95% confident the population proportion is within 6.8% of 60% (Correct answer)
- 6.8% of students were incorrectly surveyed
Correct answer: We are 95% confident the population proportion is within 6.8% of 60%
The margin of error defines the range around the sample statistic within which we are 95% confident the true parameter lies.
AP Stats Stats: Evaluation Overview 2
A researcher wants to test whether a new drug reduces blood pressure.
Which type of study provides the strongest evidence of causation?