AP®StatisticsCollege BoardExam QuestionsUnit 3: Inference for Categorical Data: ProportionsIntroduction to Hypothesis Testing & Confidence Intervals

Introduction to Hypothesis Testing & Confidence Intervals (College Board AP® Statistics): Exam Questions

Syllabus Edition

First teaching 2026

First exams 2027

5 mins5 questions
1
Sme Calculator
1 mark

A hypothesis test was conducted on a set of data from an experiment, and a 95% confidence interval was constructed about the sample statistic. If the same experiment was repeated with a larger sample size and the sample statistic was calculated to be the same value, which of the following statements is true about the new confidence interval that they could have obtained?

  • The confidence interval would be smaller and would be centered around the same value.

  • The confidence interval would be larger and would be centered around the same value.

  • The confidence interval would be the same size and would be centered around the same value.

  • The confidence interval would be the same size and would be centered around a smaller value.

Choose your answer

2
Sme Calculator
1 mark

A hypothesis test is conducted on a set of data at a 1% significance level, which results in a p-value of 0.0043. Which of the following statements about the hypotheses is true?

  • There is sufficient evidence to reject the null hypothesis.

  • There is not sufficient evidence to reject the null hypothesis.

  • There is sufficient evidence to accept the null hypothesis.

  • There is sufficient evidence to accept the alternative hypothesis.

Choose your answer

3
Sme Calculator
1 mark

A two-tailed hypothesis test was conducted on the results of an experiment. A p-value of 0.36 was obtained. If the person performing the experiment had conducted a one-tailed test on the same results, which of the following statements is true about the possible p-value(s) that they could have obtained?

  • The only possible p-value is 0.18.

  • The only possible p-value is 0.36.

  • The possible p-values are 0.18 and 0.72.

  • The possible p-values are 0.18 and 0.82.

Choose your answer

4
Sme Calculator
1 mark

The p-value for a one-tailed hypothesis test is 0.22. If the test had been two-tailed, what would the p-value(s) have been?

  • The only possible p-value is 0.11.

  • The only possible p-value is 0.22.

  • The only possible p-value is 0.44.

  • The possible p-values are 0.11 and 0.44.

Choose your answer

5
Sme Calculator
1 mark

A one-sample, two-tailed z-test is performed on a set of data. The test statistic produced by the hypothesis test is 80%, and the standard error is square root of 1 over 3125 end root.

If the reported percent has a margin of error of 3.5 percentage points, which of the following is closest to the level of confidence?

  • 90.0%

  • 95.0%

  • 97.5%

  • 99.0%

Choose your answer