AP Statistics Means Test with Answers – Free PDF

Contents

This ap statistics means test checks inference for means in 45 minutes, with 9 questions for a total of 20 points.

Answer all nine questions in 45 minutes. Show hypotheses, conditions, calculations and conclusions in context, as on the free-response section of the AP exam. A calculator is allowed. The test is worth 20 points.

Test information

Grade: AP Statistics
Chapter: Inference for Means
Common Core: AP Statistics Unit 4 (2026-27)
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 3 pts; Question 3: 3 pts; Question 4: 2 pts; Question 5: 3 pts; Question 6: 3 pts; Question 7: 2 pts; Question 8: 1 pt; Question 9: 1 pt)

AP Statistics Means Test: questions 1–5

Question 1: Checking conditions (2 points)

A random sample of 15 values (a small part of a large population) is shown. An analyst wants to build a t interval for the population mean. Decide whether the conditions for the interval are satisfied and justify the answer.

Fifteen randomly selected values.

Question 2: Interval for one mean (3 points)

A random sample of 9 sealed jars of honey from a large production run has weights (pounds) \(3.4, 3.8, 3.1, 3.6, 3.9, 3.3, 3.5, 3.7, 3.2\). A dot plot shows no outliers or strong skewness.

Construct a 95% confidence interval for the mean weight of all jars. (2 points)
Interpret the interval in context. (1 point)

Question 3: Significance test for one mean (3 points)

A cafe claims that its cold-brew cups hold a mean of 12.5 ounces. Aisha suspects the cups hold less. She measures a random sample of 20 cups (a small part of the cafe’s output) and finds \(\,\overline{x}=11.4\) ounces and \(s=2.4\) ounces. A graph shows no strong skewness or outliers. Do the data provide convincing evidence that the mean is less than 12.5 ounces? Use \(\alpha=0.05\).

Question 4: Claim and confidence interval (2 points)

A company claims its batteries last a mean of 40 hours. A 95% confidence interval for the true mean, computed from a random sample, is \((36.2, 39.4)\) hours.

Does the interval provide convincing evidence that the mean is not 40 hours? Justify the answer. (1 point)
Would a two-sided test of \(H_0: \mu=38\) at \(\alpha=0.05\) reject \(H_0\)? Explain. (1 point)

Question 5: Paired data (3 points)

Eight randomly selected patients have their systolic blood pressure (mm Hg) measured before and after a month of a new diet. The data and a dot plot of the differences (before minus after) are shown. Do the data provide convincing evidence that the diet lowers mean blood pressure? Use \(\alpha=0.05\).

Patient	1	2	3	4	5	6	7	8
Before	112	98	125	104	131	109	118	101
After	105	95	117	103	120	104	110	100

Differences (before minus after) in mm Hg.

AP Statistics Means Test: questions 6–9

Question 6: Two independent means (3 points)

Noah randomly chooses a route to school on each of 23 mornings: 12 times Route 1 and 11 times Route 2. His travel times (minutes) are shown in the box plots.

Route 1: 68, 72, 75, 70, 66, 74, 71, 69, 73, 77, 67, 72

Route 2: 64, 70, 67, 63, 69, 66, 72, 65, 68, 62, 71

Travel times (minutes) on two routes.

Do the data provide convincing evidence of a difference in the mean travel times of the two routes? Use \(\alpha=0.05\).

Question 7: Choosing a procedure (2 points)

Name the appropriate inference procedure for each situation. Do not carry out the procedure.

A random sample of 40 adults is asked whether they own an e-reader; the goal is to estimate the proportion of all adults who do. (1 point)
The same 15 customers are timed at self-checkout and at a staffed lane in random order; the goal is to compare mean times . (1 point)

Question 8: t versus z (1 point)

For a 95% confidence level and a sample of size 12, explain why the critical value \(t^{*}\) is larger than \(z^{*}=1.960\).

Question 9: Sample size and interval width (1 point)

Two random samples from the same population have the same mean and the same standard deviation, with \(n=16\) and \(n=64\). Which 95% t interval for the mean is narrower, and why?