AP®StatisticsCollege BoardExam QuestionsUnit 3: Inference for Categorical Data: ProportionsErrors in Hypothesis Tests

Errors in Hypothesis Tests (College Board AP® Statistics): Exam Questions

Syllabus Edition

First teaching 2026

First exams 2027

5 mins5 questions
1
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1 mark

An antibiotic is be given to an individual by a nurse if the nurse suspects that the individual has pneumonia. The decision-making process is represented by the null hypothesis and the alternative hypothesis below.

straight H subscript 0 colon The individual does not have pneumonia.

straight H subscript straight a colon The individual does have pneumonia.

Which of the following situations describes a Type II error being made?

  • The nurse diagnoses an individual as having pneumonia when the individual does not have pneumonia.

  • The nurse diagnoses an individual as having pneumonia when the individual has pneumonia.

  • The nurse fails to diagnose an individual as having pneumonia when the individual has pneumonia.

  • The nurse gives the antibiotic regardless of whether the individual has or does not have pneumonia.

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2
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1 mark

A quality control inspector checks a large batch of yogurts by taking a random sample of yogurts and performing a test to see if they are a good quality batch or a bad quality batch. The decision made can be represented by the following null and alternative hypotheses.

straight H subscript 0 colon The batch of yogurts is a good quality batch.

straight H subscript straight a colon The batch of yogurts is a bad quality batch.

Which of the following situations describes a Type I error being made?

  • The batch of yogurts is determined by the inspector to be of good quality when the batch is of bad quality.

  • The batch of yogurts is determined by the inspector to be of good quality when the batch is of good quality.

  • The inspector is unable to determine whether the batch of yogurts is of good quality or of bad quality.

  • The batch of yogurts is determined by the inspector to be of bad quality when the batch is of good quality.

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3
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A hypothesis test is conducted for a population mean, \mu, with a given significance level, \alpha, and sample size, n. The null and the alternative hypotheses are shown below.

H_{0} : \mu = 6.5

H_{a} : \mu < 6.5

Assuming that the alternative hypothesis is true and that the actual mean is known, which value for the actual mean below gives the greatest power of the test?

  • 7

  • 6.5

  • 6

  • 5

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4
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A hospital will stop prescribing a new medication if the director of the hospital suspects that over 10% of patients receiving the new medication are experiencing side effects. They will take a random sample of n patients from the hospital who used the new medication and count the number of patients who experienced side effects. A hypothesis test will be performed at the 5% significance level using the following hypotheses:

straight H subscript 0 colon The percentage of patients at the hospital experiencing side effects from the new medication is 10%

straight H subscript straight a colon The percentage of patients at the hospital experiencing side effects from the new medication is greater than 10%

For which of the following cases would the power of the test be the greatest?

  • The size of the random sample is n = 800, and 30% of all patients from the hospital who take the new medication experience side effects.

  • The size of the random sample is n = 800, and 10% of all patients from the hospital who take the new medication experience side effects.

  • The size of the random sample is n = 400, and 10% of all patients from the hospital who take the new medication experience side effects.

  • The size of the random sample is n = 400, and 30% of all patients from the hospital who take the new medication experience side effects.

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5
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A hypothesis test has a significance level of alpha and a one-sided alternative hypothesis. It is known that the null hypothesis is false. If the significance level were halved to alpha over 2, which of the following statements would be true?

  • Both the power of the test and the probability of a Type II error would increase.

  • The power of the test would increase, and the probability of a Type II error would decrease.

  • The power of the test would decrease, and the probability of a Type II error would increase.

  • The power of the test and the probability of a Type II error would remain unchanged.

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