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

Inference for Means (College Board AP® Statistics)

Exam Questions

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1
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A researcher wants to estimate the difference between the mean life expectancies of orcas and beluga whales. A random sample of 15 orcas has a mean life expectancy of 57.2 years and a standard deviation of 4.8 years. A random sample of 15 beluga whales has a mean life expectancy of 49.1 years and a life expectancy of 6.3 years. What is the standard error of the difference (orca - beluga) between the sample means?

  • square root of fraction numerator open parentheses 4.8 close parentheses squared plus left parenthesis 6.3 right parenthesis squared over denominator 30 end fraction end root

  • square root of fraction numerator open parentheses 4.8 close parentheses squared minus left parenthesis 6.3 right parenthesis squared over denominator 30 end fraction end root

  • square root of fraction numerator open parentheses 4.8 close parentheses squared plus left parenthesis 6.3 right parenthesis squared over denominator 15 end fraction end root

  • square root of fraction numerator open parentheses 4.8 close parentheses squared minus left parenthesis 6.3 right parenthesis squared over denominator 15 end fraction end root

  • square root of fraction numerator open parentheses 4.8 close parentheses minus left parenthesis 6.3 right parenthesis over denominator 15 end fraction end root

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2
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An electric car battery manufacturer claims that their batteries have a lifespan of 5.7 years. A mechanic specializing in electric cars believes that this claim is unrealistic and that the actual lifespan is less than 5.7 years. The mechanic decides to conduct a study to investigate the situation. Which of the following hypotheses should be tested?

  • straight H subscript 0 colon space x with bar on top equals 5.7 and straight H subscript straight a colon space x with bar on top not equal to 5.7

  • straight H subscript 0 colon space x with bar on top equals 5.7 and straight H subscript straight a colon space x with bar on top less than 5.7

  • straight H subscript 0 colon space x with bar on top equals 5.7 and straight H subscript straight a colon space x with bar on top greater than 5.7

  • straight H subscript 0 colon space mu equals 5.7 and straight H subscript straight a colon space mu less than 5.7

  • straight H subscript 0 colon space mu equals 5.7 and straight H subscript straight a colon space mu greater than 5.7

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3
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An experiment is conducted to test whether listening to classical music while completing a math quiz has an impact on the score achieved. Thirty-six volunteers are randomly selected and assigned to either take the quiz in silence or to take the quiz while listening to classical music. There is an equal number of volunteers in each group. The mean quiz score for each group is calculated, and a two-sample confidence interval for the difference of the means is to be calculated. Which of the following assumptions is required for the confidence interval to be valid?

  • Each of the two groups has at least five successes and five failures.

  • The sample size is less than ten percent of the population size.

  • The distributions of test scores of the two groups are approximately uniformly distributed.

  • The volunteers in the group taking the quiz in silence are paired with the volunteers taking the quiz while listening to classical music.

  • The expected number of people who pass the quiz in each group must be at least five.

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4
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A random sample of 40 teenagers from a large population resulted in a 95% confidence interval for the mean number of minutes spent on social media per day of left parenthesis 158 comma space 170 right parenthesis. Which of the following best summarizes the meaning of this confidence interval?

  • A teenager selected at random from this population spends between 158 and 170 minutes per day on social media for 95% of days.

  • 95% of teenagers from the population spend between 158 and 170 minutes on social media per day.

  • 95% of teenagers from the sample reported spending between 158 and 170 minutes per day on social media.

  • About 95% of all random samples of 40 teenagers from this population would result in a 95% confidence interval of left parenthesis 158 comma space 170 right parenthesis.

  • About 95% of all random samples of 40 teenagers from this population would result in a 95% confidence interval that covered the population mean number of minutes spent on social media per day.

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5
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A magazine that tests and reviews different products decided to conduct a double-blind experiment on the effectiveness of two different types of blenders. They believed that blender A would take less time to blend vegetables than blender B. Twelve people were randomly selected to test either blender A or blender B. They were asked to record in seconds the time it took to blend four cups of chopped and boiled carrots into a smooth puree. The following day, they were asked to repeat the test with the other blender. All branding was removed from the blenders, so they did not know which blender they had used at either time. The table below shows the summary statistics for the results.

Seconds until blended

Difference (blender A - blender B)

Blender A

Blender B

Mean

22.350

23.658

-1.308

Standard deviation

4.667

5.123

1.487

Which of the following values is closest to the p-value of the appropriate t-test?

  • 0.994

  • 0.260

  • 0.043

  • 0.011

  • 0.006

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