AP Statistics Practice Quiz: Setting Up a Test for a Population Mean

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

A researcher wants to conduct a hypothesis test for a population mean, but the population standard deviation (sigma) is not known. According to the provided content, what is the appropriate testing method?

A)A one-sample z-testB)A one-sample t-testC)A two-sample t-testD)A chi-squared test

All Questions (16)

A) A one-sample z-test

B) A one-sample t-test

C) A two-sample t-test

D) A chi-squared test

Correct Answer: B

The provided content explicitly states, 'The appropriate test for a population mean with unknown sigma is a one-sample t-test.'

When setting up a one-sample t-test for a population mean, what is the general form of the null hypothesis?

A) H0: mu ≠ mu0

B) H0: mu > mu0

C) H0: mu = mu0

D) H0: p = p0

Correct Answer: C

The content specifies that 'The null hypothesis for a one-sample t-test is H0: mu = mu0,' where mu0 represents the hypothesized value of the population mean.

A study is designed to test the effectiveness of a new diet plan by measuring the weight of 25 participants before and after the plan. How should this matched pairs data be analyzed?

A) With a two-sample t-test on the 'before' and 'after' weights.

B) With a one-sample z-test on the mean weight.

C) With a one-sample t-test on the differences in weight for each participant.

D) By comparing the standard deviation of the 'before' and 'after' weights.

Correct Answer: C

The provided text states, 'Matched pairs data can be analyzed with a one-sample t-test on the differences.' This involves calculating the difference for each pair and then performing a one-sample t-test on those calculated differences.

Before performing a t-test for a population mean, what two main conditions must be verified?

A) The sample size must be greater than 100 and the data must be categorical.

B) The population standard deviation must be known and the sample must be large.

C) The data must come from a convenience sample and the population must be skewed.

D) The independence condition must be met and the sampling distribution must be approximately normal.

Correct Answer: D

The content clearly states that to test a population mean, one must 'check for independence and that the sampling distribution is approximately normal.'

A company claims its batteries last for an average of 300 hours. A consumer group wants to test if the actual average lifespan is less than 300 hours. What are the correct null and alternative hypotheses?

A) H0: mu = 300, Ha: mu ≠ 300

B) H0: mu = 300, Ha: mu < 300

C) H0: mu < 300, Ha: mu = 300

D) H0: p = 300, Ha: p < 300

Correct Answer: B

The null hypothesis is a statement of no effect or no difference, so H0: mu = 300. The consumer group is testing if the mean is 'less than' the claimed value, which translates to the alternative hypothesis Ha: mu < 300.

When analyzing matched pairs data, such as the change in blood pressure after a medication, why is it important to define the order of subtraction (e.g., 'after' - 'before')?

A) It determines whether a t-test or a z-test should be used.

B) It is necessary to satisfy the independence condition for the test.

C) It determines the sign of the mean difference and the direction of the alternative hypothesis.

D) It is required to calculate the degrees of freedom for the test.

Correct Answer: C

The content highlights that 'it is important to define the order of subtraction for the mean difference.' This is because the direction of the subtraction (e.g., after - before vs. before - after) determines whether an increase corresponds to a positive or negative difference, which directly impacts the formulation of the alternative hypothesis (e.g., Ha: mu_diff > 0 vs. Ha: mu_diff < 0).

Which of the following scenarios is best analyzed using a one-sample t-test for a mean difference?

A) Comparing the average income of residents in two different cities.

B) Testing if the proportion of students who pass an exam is greater than 80%.

C) Evaluating the change in test scores for a group of students who took a pre-test and a post-test.

D) Comparing the average height of a random sample of men to a random sample of women.

Correct Answer: C

The scenario in option C is a classic matched pairs design, where each student has a paired pre-test and post-test score. The content specifies that 'Matched pairs data can be analyzed with a one-sample t-test on the differences.'

A researcher tests if a new fertilizer increases the average yield of corn. They measure the yield of 35 plots of land before and after applying the fertilizer. They define the difference as (yield after - yield before). What would be the null hypothesis for this test?

A) H0: mu_diff = 0

B) H0: mu_diff > 0

C) H0: mu_1 = mu_2

D) H0: mu = 35

Correct Answer: A

This is a matched pairs test on the differences. The null hypothesis assumes no effect or no change. In this context, no change in yield would mean the average difference between the 'after' and 'before' measurements is zero. Therefore, H0: mu_diff = 0.

The primary reason for using a t-test instead of a z-test for a population mean is that...

A) the sample size is small.

B) the population standard deviation (sigma) is unknown.

C) the data is from a matched pairs design.

D) the sampling distribution is not normal.

Correct Answer: B

The provided content consistently identifies the condition for using this test as having an 'unknown sigma.' A one-sample t-test is the appropriate method for a population mean specifically when the population standard deviation is unknown.

In the hypothesis H0: mu = 50, what does the value '50' represent?

A) The sample mean.

B) The population standard deviation.

C) The sample size.

D) The hypothesized value of the population mean.

Correct Answer: D

The content defines the null hypothesis as H0: mu = mu0. In this structure, mu represents the true population mean, and mu0 represents the specific value being tested, which is the hypothesized population mean.

A test is conducted to see if a specific training program improves employee productivity. Productivity is measured for 40 employees before and after the program. The alternative hypothesis is Ha: μ_d > 0, where d = (productivity after - productivity before). What does this alternative hypothesis suggest?

A) The training program has no effect on productivity.

B) The training program decreases employee productivity on average.

C) The training program changes employee productivity, but the direction is unknown.

D) The training program increases employee productivity on average.

Correct Answer: D

Since the difference is defined as 'after - before', a positive difference (d > 0) means the 'after' score is higher than the 'before' score. Therefore, the alternative hypothesis Ha: μ_d > 0 is testing the claim that the mean difference is positive, which implies that productivity, on average, has increased.

When performing a one-sample t-test on matched pairs data, what is the actual data set that is being tested?

A) The set of all 'before' measurements.

B) The set of all 'after' measurements.

C) The set of calculated differences between the paired measurements.

D) The average of the 'before' and 'after' measurements.

Correct Answer: C

The content explicitly states that 'Matched pairs data can be analyzed with a one-sample t-test on the differences.' This means the primary data for the test is the single sample of differences calculated from the pairs.

Which of the following is a required step in setting up a test for a population mean with an unknown sigma?

A) Proving that the population distribution is exactly normal.

B) Calculating the population standard deviation, sigma.

C) Verifying that the sampling distribution of the mean is approximately normal.

D) Ensuring the sample size is smaller than 30.

Correct Answer: C

The provided content lists verifying conditions as a key step. Specifically, it says to 'check for independence and that the sampling distribution is approximately normal.' This is a required check before proceeding with the test.

A school administrator wants to test if the average student GPA is different from 3.0. They take a random sample of 50 students and find the sample mean GPA. The population standard deviation of GPAs is unknown. Which is the correct identification of the test and the null hypothesis?

A) One-sample t-test; H0: μ = 3.0

B) One-sample z-test; H0: μ = 3.0

C) Matched pairs t-test; H0: μ_d = 3.0

D) One-sample t-test; H0: p = 3.0

Correct Answer: A

Because the population standard deviation (sigma) is unknown, a one-sample t-test is the appropriate method. The null hypothesis tests the claim that the population mean is equal to a specific value, so H0: μ = 3.0 is correct.

The process of analyzing matched pairs data by first calculating the difference for each pair effectively transforms the problem into which type of test?

A) A two-sample problem comparing two independent means.

B) A one-sample problem for a single population mean (of differences).

C) A problem of comparing two population proportions.

D) A test for which the population standard deviation must be known.

Correct Answer: B

The content states that 'Matched pairs data can be analyzed with a one-sample t-test on the differences.' By taking the differences, we create a single sample of data points (the differences), which we then analyze as a one-sample test for a population mean.

To perform a valid t-test for a population mean, besides checking for approximate normality of the sampling distribution, what other condition must be checked?

A) The sample size must be exactly 30.

B) The data must be paired.

C) The independence of the observations.

D) The null hypothesis must be true.

Correct Answer: C

The provided content lists the two conditions to check as 'independence and that the sampling distribution is approximately normal.' Therefore, independence is the other required condition.