AP Statistics Sampling Distributions and the Central Limit Theorem Test with Point Values (PDF)

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

Cover of the book AP Statistics Math Tests with Answer Keys (PDF)

Download as a PDFThe AP Statistics tests book with answer keysPrintable PDFSee the book ›

Sommaire

This sampling distributions test 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.

This 45-minute test covers sampling distributions for proportions and means, conditions, the central limit theorem, and differences. Show the mean, the standard deviation, and the conditions before every probability.

Time and points

About this test

Grade: AP Statistics
Chapter: Sampling Distributions and the Central Limit Theorem
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
Time: 45 minutes
Total: 20 points

Sampling distributions test: questions

Question 1 – Proportion probability [4 pts]

Sampling distribution of p-hat.

In a population, 30% of people are left-handed or ambidextrous. A random sample of 100 is taken. (a) Find the mean and standard deviation of p-hat. (2 points) (b) Check the conditions for a normal model. (1 point) (c) Find P(p-hat > 0.35). (1 point)

Question 2 – Sample mean [3 pts]

Waiting times at a drive-through have mean 4.2 minutes and sd 1.5 minutes (skewed right). A random sample of 36 customers is taken. (a) Describe the sampling distribution of x-bar. (2 points) (b) Find P(x-bar > 4.6). (1 point)

Question 3 – Effect of n [2 pts]

For p = 0.5, find the standard deviation of p-hat for n = 100 and n = 400, and state how much the spread decreases.

Question 4 – Bias and variability [2 pts]

Sketch in words two sampling distributions: one unbiased with high variability, one biased with low variability. Which is better and why?

Question 5 – Difference of proportions [3 pts]

Independent random samples of 80 boys (p = 0.5 own a bike) and 100 girls (p = 0.4 own a bike) are taken. Find the mean and standard deviation of p-hat boys minus p-hat girls. (3 points)

Question 6 – Poll probability [2 pts]

Sampling distribution, n = 100.

A candidate has true support of 50%. In a random sample of 100 voters, find the probability that fewer than 42% support the candidate.

Question 7 – Conditions [2 pts]

A researcher wants to model the sample proportion for n = 30 and p = 0.05. Check the normality condition and conclude.

Question 8 – Within two standard errors [2 pts]

Sampling distribution of the mean for n = 16.

A normal population has mean 50 and sd 12. For n = 16, find the interval that contains about 95% of sample means.

Key facts behind this sampling distributions test

Key facts

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 test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

Voter.. post

Free printable PDF