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AP®StatisticsCollege BoardExam QuestionsUnits 6-9: InferenceInference for Regression Slopes

Inference for Regression Slopes (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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Research shows that there is a positive linear relationship between the number of hours of sleep and the scores on an exam. A linear regression analysis was performed on a random sample of 20 students, with the results shown below.

Predictor

Coef

SE Coef

T

P

Constant

23.532

3.573

6.59

0.000

Hours

5.492

0.1735

31.65

0.001

S = 85.325

R-Sq = 75.3 %

R-Sq (adj) = 72.9 %

It is known that all conditions for inference were met. Which of the following shows a 95% confidence interval for the slope of the least-squares regression line?

  • 23.532 plus-or-minus 2.101 open parentheses 3.573 close parentheses

  • 5.492 plus-or-minus 2.101 open parentheses 0.1735 close parentheses

  • 5.492 plus-or-minus 2.101 open parentheses 85.325 close parentheses

  • 23.532 plus-or-minus 2.101 open parentheses fraction numerator 85.325 over denominator square root of 20 end fraction close parentheses

  • 5.492 plus-or-minus 2.101 open parentheses fraction numerator 0.1735 over denominator square root of 20 end fraction close parentheses

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2
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A linear relationship is assumed between a fox's tail length and its weight. A forest ranger captures 27 foxes and measures their tail length in inches (in) and their weight in pounds (lb). The data gathered was used to generate the computer output below.

Predictor

Coef

SE Coef

T

P

Constant

2.361

1.281

1.84

0.000

Length

0.120

0.0313

3.83

0.003

S = 101.312

R-Sq = 65.2 %

R-Sq (adj) = 63.1 %

Given that all conditions for inference are met, which of the following shows a 90% confidence interval estimate of the slope of the population regression line for predicting weight from tail length?

  • 0.120 plus-or-minus 1.703 open parentheses 0.0313 close parentheses

  • 0.120 plus-or-minus 2.060 open parentheses 0.0313 close parentheses

  • 0.120 plus-or-minus 1.645 open parentheses 0.0313 close parentheses

  • 0.120 plus-or-minus 3.83 open parentheses 0.0313 close parentheses

  • 0.120 plus-or-minus 1.708 open parentheses 0.0313 close parentheses

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3
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A theme park is investigating the relationship between the number of daily visitors (in thousands) and the daily temperature (in °F). A regression analysis was conducted on a random sample of 14 days in the year, and the computer output is given below.

Predictor

Coef

SE Coef

T

P

Constant

2.891

1.281

2.26

0.000

Temp

0.215

0.121

1.78

0.001

S = 5.233

R-Sq = 71.6 %

R-Sq (adj) = 71.1 %

Given that all conditions for inference are met, which of the following gives the margin of error of a 95% confidence interval for the slope of the least-squares regression line for the data?

  • open parentheses 2.179 close parentheses open parentheses 0.121 close parentheses

  • open parentheses 2.179 close parentheses open parentheses fraction numerator 0.121 over denominator square root of 12 end fraction close parentheses

  • open parentheses 2.179 close parentheses open parentheses 5.233 close parentheses

  • open parentheses 2.179 close parentheses open parentheses fraction numerator 5.233 over denominator square root of 12 end fraction close parentheses

  • open parentheses 2.179 close parentheses open parentheses 0.215 close parentheses

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4
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A 95% confidence interval for the slope of a regression line is calculated, giving open parentheses negative 0.091 comma space 0.413 close parentheses. Which of the following statements is true?

  • The association shown on a scatterplot is linear.

  • The slope of the sample regression line is 0.322.

  • There is evidence that the slope of the sample regression line is 0.

  • The correlation coefficient of the data is positive.

  • The sum of the residuals of the data using the regression line is positive.

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5
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An investigation is conducted into a possible negative linear association between life expectancy and the number of cigarettes smoked per day. The results from a random sample of 15 people are summarized in the table below.

Predictor

Coef

SE Coef

T

P

Constant

86.3

1.387

62.2

0.000

Number

-0.893

0.091

-9.81

0.002

S = 3.213

R-Sq = 82.8 %

R-Sq (adj) = 80.2 %

In order to test the null hypothesis that the slope of the population regression line is zero, which of the following values gives the correct test statistic? You may assume that all conditions for inference are met.

  • fraction numerator 86.3 over denominator 1.387 end fraction

  • fraction numerator 86.3 over denominator open parentheses fraction numerator 1.387 over denominator square root of 15 end fraction close parentheses end fraction

  • fraction numerator negative 0.893 over denominator 3.213 end fraction

  • fraction numerator negative 0.893 over denominator 0.091 end fraction

  • fraction numerator 0.893 over denominator 0.091 end fraction

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