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AP®StatisticsCollege BoardExam QuestionsUnits 6-9: InferenceErrors in Hypothesis Tests

Errors in Hypothesis Tests (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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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 fails to diagnose an individual as having pneumonia when the individual does not have 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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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 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 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 equals 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 equals 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 equals 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 equals 400, and 30% of all patients from the hospital who take the new medication experience side effects.

  • The size of the random sample is n equals 200, and 30% of all patients from the hospital who take the new medication experience side effects.

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4
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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.

straight H subscript 0 colon space straight mu equals 6.5 straight H subscript straight a colon space mu less than 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?

  • 10

  • 7

  • 6.5

  • 6

  • 5

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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.

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

  • 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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