Some questions of the AP Statistics exam test your knowledge of sampling distributions: sampling distribution of a
sample proportion, sample distribution of a sample mean, the Central Limit Theorem, sampling distribution of a
difference between two independent sample proportions, sample distribution of a difference between two independent sample means,
simulation of sampling distributions, t-distribution, Chi-square distribution.
Examples of AP Statistics multiple choice questions with sampling distributions:
1.Out of the 500 students of a school, 30% wear glasses. If we use a simple random sample of 25 students, which
of the following statements is correct:
a) The sampling distribution is small relative to the population. b) The sampling distribution is a skewed distribution. c) The sampling distribution is normal. d) The mean of the sampling distribution is μ = .3. e) None of the above.
The distribution of the data exhibits skewness because n·p = 25·.3 < 10, so b) is the correct answer.
2. A large automobile manufacturer states that approximately 4% of all their cars made in 2010 have a
defective component. Two samples of 150 cars (sample A) and 250 cars (sample B) were taken to test for the defective component.
Which of the following statements must be true?
a) The standard deviation of the sample A < the standard deviation of the sample B. b) The mean of the sample A < the mean of the sample B. c) Both samples will have equal standard deviations. d) The mean of the sample A > the mean of the sample B. e) The standard deviation of the sample A > the standard deviation of the sample B.
The standard deviation gets smaller as the size of the sample increases. Answer e) is correct.