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

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

According to the provided content, which of the following represents the standard form for a null hypothesis for a population proportion?

A)H0: p > p0B)H0: p < p0C)H0: p = p0D)H0: p ≠ p0

All Questions (16)

According to the provided content, which of the following represents the standard form for a null hypothesis for a population proportion?

A) H0: p > p0

B) H0: p < p0

C) H0: p = p0

D) H0: p ≠ p0

Correct Answer: C

The content explicitly states in point 6 that 'The null hypothesis for a population proportion is H0: p = p0.' The null hypothesis always contains a form of equality.

A researcher wants to test if the proportion of adults who own a smartphone is different from the previously reported value of 0.85. What is the appropriate alternative hypothesis for this test?

A) Ha: p < 0.85

B) Ha: p > 0.85

C) Ha: p = 0.85

D) Ha: p ≠ 0.85

Correct Answer: D

The phrase 'different from' indicates a two-sided test. According to point 7, a two-sided alternative hypothesis for a proportion takes the form p ≠ p0.

What is the appropriate statistical test to use when investigating a claim about a single categorical variable's population proportion?

A) A one-sample t-test for a mean

B) A one-sample z-test for a proportion

C) A chi-squared test for independence

D) A two-sample z-test for proportions

Correct Answer: B

Point 9 states that 'The appropriate test for a single categorical variable's population proportion is a one-sample z-test.'

When setting up a hypothesis test for a population proportion, what is the fundamental assumption made about the null hypothesis?

A) It is assumed to be incorrect until proven otherwise.

B) It is assumed to be correct unless evidence suggests otherwise.

C) It is assumed to be equal to the sample proportion.

D) It is assumed to be less than the alternative hypothesis value.

Correct Answer: B

Point 4 clearly states, 'The null hypothesis is assumed to be correct unless evidence suggests otherwise.' This is a foundational principle of hypothesis testing.

A school claims that more than 70% of its students participate in extracurricular activities. If 'p' represents the true proportion of students who participate, which of the following is the correct alternative hypothesis to test this claim?

A) Ha: p < 0.70

B) Ha: p = 0.70

C) Ha: p > 0.70

D) Ha: p ≠ 0.70

Correct Answer: C

The claim being tested is that the proportion is 'more than' 70%. The alternative hypothesis is what is being tested for. According to point 7, a one-sided alternative for 'greater than' is p > p0.

When verifying the conditions for a one-sample z-test for a proportion, the check for an approximately normal sampling distribution must be performed under what key assumption?

A) Assuming the alternative hypothesis is true.

B) Assuming the sample proportion is the true proportion.

C) Assuming the null hypothesis is true.

D) Assuming the population is perfectly normal.

Correct Answer: C

Point 10 specifies that to test a population proportion, one must check that the sampling distribution is approximately normal, 'assuming H0 is true.' This is a critical detail in verifying conditions.

Which of the following statements correctly distinguishes between the null and alternative hypotheses based on the symbols they contain?

A) The null hypothesis contains a strict inequality (<, >), while the alternative contains an equality (=).

B) Both the null and alternative hypotheses contain strict inequalities.

C) The null hypothesis contains an equality (=, >=, <=), while the alternative contains a strict inequality (<, >, ≠).

D) Both the null and alternative hypotheses contain forms of equality.

Correct Answer: C

This is a direct application of point 5, which states: 'The null hypothesis contains an equality (=, >=, <=), while the alternative contains a strict inequality (<, >, !=).'

A consumer advocacy group believes the proportion of defective widgets produced by a factory is less than the 5% advertised. What is the null hypothesis for this test?

A) H0: p = 0.05

B) H0: p < 0.05

C) H0: p > 0.05

D) H0: p ≠ 0.05

Correct Answer: A

Even though the claim being tested is 'less than 5%', the null hypothesis must contain the statement of equality. According to points 6 and 8, the null hypothesis specifies a single value for the population proportion, so H0: p = 0.05 is the correct form.

Which two conditions must be verified before making statistical inferences when testing a population proportion?

A) Randomness and a large population size.

B) A symmetric sample distribution and a known population standard deviation.

C) Independence and an approximately normal sampling distribution.

D) A large sample size and a two-sided alternative hypothesis.

Correct Answer: C

Point 10 states that to test a population proportion, one must 'check for independence and that the sampling distribution is approximately normal.'

In the context of hypothesis testing for a proportion, what does the alternative hypothesis represent?

A) The hypothesis that is assumed to be correct by default.

B) The hypothesis that always contains a statement of equality.

C) The hypothesis that is being tested for.

D) The hypothesis that represents the historical value of the proportion.

Correct Answer: C

Point 4 defines the alternative hypothesis as 'what is being tested for.' It represents the claim or effect that the researcher is trying to find evidence to support.

Which of the following pairs represents a valid set of null and alternative hypotheses for a one-sample z-test for a proportion?

A) H0: p = 0.5 vs. Ha: p ≠ 0.6

B) H0: p ≠ 0.5 vs. Ha: p = 0.5

C) H0: p = 0.5 vs. Ha: p > 0.5

D) H0: p > 0.5 vs. Ha: p < 0.5

Correct Answer: C

A valid set of hypotheses must test the same population proportion value (p0). The null hypothesis must contain equality (H0: p = p0), and the alternative must contain a strict inequality. Option C is the only one that follows these rules from points 5 and 6.

For a one-sample z-test for a proportion, the null hypothesis serves to:

A) prove that the sample result is correct.

B) specify a value for the population proportion to test against.

C) determine the direction of the test (one-sided or two-sided).

D) confirm that the independence condition has been met.

Correct Answer: B

Point 8 states, 'For a one-sample z-test for a proportion, the null hypothesis specifies a value for the population proportion.' This value, p0, is the benchmark against which the sample evidence is measured.

A political analyst is testing if a candidate's approval rating is no longer 40%. Which of the following is an error in setting up the test?

A) Choosing a one-sample z-test as the appropriate method.

B) Setting the null hypothesis as H0: p = 0.40.

C) Setting the alternative hypothesis as Ha: p ≠ 0.40.

D) Setting the null hypothesis as H0: p ≠ 0.40.

Correct Answer: D

According to point 5, the null hypothesis must contain a form of equality. Setting the null hypothesis with a strict inequality (≠) is incorrect. The alternative hypothesis is the one that contains the strict inequality.

The primary goal of verifying conditions before conducting a one-sample z-test for a proportion is to:

A) prove the null hypothesis is true.

B) ensure the sample size is greater than 30.

C) determine the correct alternative hypothesis.

D) ensure that making statistical inferences is valid.

Correct Answer: D

Point 3 states the need to 'Verify the conditions for making statistical inferences when testing a population proportion.' The purpose of checking conditions is to ensure that the results of the test are reliable and that the inferential procedure is appropriate.

Which of the following is NOT a possible form for an alternative hypothesis for a population proportion?

A) Ha: p < p0

B) Ha: p > p0

C) Ha: p ≠ p0

D) Ha: p = p0

Correct Answer: D

Point 5 specifies that the alternative hypothesis contains a strict inequality (<, >, ≠). Point 7 lists the three possible forms. A statement of equality (p = p0) is reserved for the null hypothesis.

A study is designed to determine if the proportion of people who prefer brand A coffee is less than 0.60. The null hypothesis is set as H0: p = 0.60. Why is it necessary to use p0 = 0.60 when checking the normality condition?

A) Because the normality check must always use the value from the alternative hypothesis.

B) Because the entire test procedure operates under the initial assumption that the null hypothesis is the true state of the population.

C) Because 0.60 is the most conservative value and makes the condition hardest to meet.

D) Because the sample proportion will always be very close to 0.60.

Correct Answer: B

Points 4 and 10 together provide the answer. The null hypothesis is assumed to be correct (Point 4), and the conditions, including normality, are checked assuming H0 is true (Point 10). Therefore, the value from the null hypothesis (p0 = 0.60) must be used to check the condition.