Inference for Regression Slopes (College Board AP® Statistics)

Exam Questions

5 mins5 questions

1 mark

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?

$23.532 \pm 2.101 (3.573)$
$5.492 \pm 2.101 (0.1735)$
$5.492 \pm 2.101 (85.325)$
$23.532 \pm 2.101 (\frac{85.325}{\sqrt{20}})$
$5.492 \pm 2.101 (\frac{0.1735}{\sqrt{20}})$

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1 mark

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?

$0.120 \pm 1.703 (0.0313)$
$0.120 \pm 2.060 (0.0313)$
$0.120 \pm 1.645 (0.0313)$
$0.120 \pm 3.83 (0.0313)$
$0.120 \pm 1.708 (0.0313)$

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1 mark

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?

$(2.179) (0.121)$
$(2.179) (\frac{0.121}{\sqrt{12}})$
$(2.179) (5.233)$
$(2.179) (\frac{5.233}{\sqrt{12}})$
$(2.179) (0.215)$

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1 mark

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.

$\frac{86.3}{1.387}$
$\frac{86.3}{(\frac{1.387}{\sqrt{15}})}$
$\frac{- 0.893}{3.213}$
$\frac{- 0.893}{0.091}$
$\frac{0.893}{0.091}$

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