AP Statistics Sampling Distributions and the Central Limit Theorem Quiz: 10 Questions with Explanations

AP Statistics math quiz: Sampling Distributions and the Central Limit Theorem – Maths PDF

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This sampling distributions quiz for AP Statistics covers sampling distributions and the central limit theorem (Common Core AP STAT 5.1, AP STAT 5.2, AP STAT 5.3, AP STAT 5.4, AP STAT 5.5, AP STAT 5.6, AP STAT 5.7, HSS-IC.A.1, HSS-IC.A.2), with a free PDF to print.

Ten multiple-choice questions test the center, spread, and shape of sampling distributions. Read each explanation, since the formulas look similar but the denominators differ.

AP Statistics · Common Core State Standards: AP STAT 5.1, AP STAT 5.2, AP STAT 5.3, AP STAT 5.4, AP STAT 5.5, AP STAT 5.6, AP STAT 5.7, HSS-IC.A.1, HSS-IC.A.2

Sampling distributions quiz: 10 questions

Question 1

Sampling distribution of p-hat for n = 50: mean 0.40, standard deviation 0.069.

The mean of this sampling distribution of p-hat is:

Question 2

For n = 200 the standard deviation is 0.035: quadrupling n halves the spread.

Compared with n = 50, this sampling distribution (n = 200) has:

Question 3

A skewed population.

For samples of size 100 from this population, the distribution of x-bar is:

Question 4

The standard deviation of x-bar for n = 49 and sigma = 14 is:

Question 5

The conditions for a normal model for p-hat include:

Question 6

For independent samples, the standard deviation of p1-hat – p2-hat is:

Question 7

Which statement about bias is true?

Question 8

When the population is normal, the sampling distribution of x-bar is normal:

Question 9

The mean of the sampling distribution of x-bar is:

Question 10

To cut the standard deviation of x-bar to one third, the sample size must be:

Remember

A sampling distribution describes how a statistic varies from sample to sample.
p-hat: mean p, sd sqrt(p(1-p)/n); approximately normal if np >= 10 and n(1-p) >= 10.
x-bar: mean mu, sd sigma/sqrt(n); normal if the population is normal or n is large (CLT).
Differences of independent statistics: means subtract, variances add.
Larger n reduces variability but never corrects bias; the 10% condition is needed for independence.

How to use this sampling distributions quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

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