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AP Statistics 9.5 Carrying Out a Test for the Slope of a Regression Model- MCQs - Exam Style Questions

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Question

A research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below.
Predictor Coef SE Coef
Constant \(88.01\) \(0.49\)
Exercise time \(-2.20\) \(0.07\)
\(S=0.76\) \(R-Sq=99.0\%\)
Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals \(0\)?
(A) \(t=\frac{88.01}{0.49}\)
(B) \(t=\frac{74.81}{7.33}\)
(C) \(t=\frac{74.81}{2.21}\)
(D) \(t=\frac{-2.20}{0.07}\)
(E) \(t=\frac{-2.20}{\frac{0.07}{\sqrt{11}}}\)
▶️ Answer/Explanation
Detailed solution

1. Test Statistic Formula for Slope:
The formula for the t-test statistic for the slope (\(b\)) of a regression line is:
\(t = \frac{\text{sample slope} – \text{hypothesized slope}}{\text{standard error of slope}} = \frac{b – \beta_0}{SE_b}\)

2. Identify Values from the Output:
– The sample slope is the coefficient for the predictor variable “Exercise time,” which is \(b = -2.20\).
– The standard error of the slope is its corresponding “SE Coef,” which is \(SE_b = 0.07\).
– The null hypothesis is that the slope equals \(0\), so \(\beta_0 = 0\).

3. Construct the Test Statistic:
\(t = \frac{-2.20 – 0}{0.07} = \frac{-2.20}{0.07}\)
✅ Answer: (D)

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