AP®StatisticsCollege BoardExam QuestionsUnits 6-9: InferenceInference for Proportions

Inference for Proportions (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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The owner of a clothing company suspects that the proportion of customers who buy scarves is greater at their Barn Street store than at their Lake Street store in January. During the month of January, the owner took a random sample of 450 customers at both locations and recorded the number of people who bought scarves at each store.

Assuming the conditions for inference are met, which of the following test procedures should be used by the owner of the clothing company?

  • A matched-pairs t-test for a mean difference

  • A one-sample t-test for a mean

  • A two-sample z-test for a difference between two proportions

  • A one-sample z-test for a proportion

  • A t-test for the slope of a regression line

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2
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A 95% confidence interval for the proportion of a city's residents who do not vote is (0.342, 0.410). What is the point estimate for the proportion of city residents who do not vote on which this interval was constructed?

  • 0.342

  • 0.376

  • 0.410

  • 0.752

  • 0.068

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3
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A random sample of 280 medical students from a university shows that 210 are interested in cardiology. What would be a 99% confidence interval for the proportion of all medical students at the university who are interested in cardiology?

  • 0.75 plus-or-minus 2.326 space square root of fraction numerator 0.75 space open parentheses 0.25 close parentheses over denominator 280 end fraction end root

  • 210 plus-or-minus 2.576 space square root of fraction numerator 0.5 space open parentheses 0.5 close parentheses over denominator 280 end fraction end root

  • 0.75 plus-or-minus 2.326 space square root of fraction numerator 0.5 space open parentheses 0.5 close parentheses over denominator 280 end fraction end root

  • 210 plus-or-minus 2.576 space square root of fraction numerator 0.75 space open parentheses 0.25 close parentheses over denominator 280 end fraction end root

  • 0.75 plus-or-minus 2.576 space square root of fraction numerator 0.75 space open parentheses 0.25 close parentheses over denominator 280 end fraction end root

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4
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A gardener is worried about a specific plant disease in their garden. From a random sample of 50 plants, the gardener will create a 90% confidence interval for the proportion of plants in their garden that have the disease. Which of the following statements is true?

  • The probability that the confidence interval will include the population proportion is 0.9.

  • The population proportion will be in the confidence interval.

  • The probability that the confidence interval will include the sample proportion is 0.9.

  • The population proportion will be equal to the sample proportion.

  • The probability that the sample proportion equals the population proportion is 0.9.

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5
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A train company's operations manager plans to take a random sample of passengers to create a 95% confidence interval and estimate the proportion of passengers who are satisfied with their recent journey. Which of the following is the smallest sample size that will result in a margin of error of no more than 7.5 percentage points?

  • 100

  • 125

  • 150

  • 175

  • 200

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