Sampling Distributions for Linear Regression Question 2

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.

\begin{array}{l l l l l} \text{Variable} \hskip{4em }& \text{N} \hskip{4em} & \text{Mean} \hskip{4em}& \text{SE Mean}\hskip{4em} & \text{StDev} \\ \text{Running Time} & 11 & 74.81 & 2.21 & 7.33 \end{array}

\begin{array}{l l l} \text{Predictor} \hskip{4em} & \text{Coef}\hskip{4em} & \text{SE Coef} \\ \text{Constant} & 88.01 & 0.49 \\ \text{Exercise Time} & -2.20 & 0.07 \\ \\ \text{S} = 0.76 & & \text{R-sq} = 99.0% \end{array}

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 ?

\dfrac{88.01}{0.49}

\dfrac{74.81}{7.33}

\dfrac{-2.20}{0.07}

\dfrac{-2.20}{\frac{0.07}{\sqrt{11}}}

Approach

Use the equation for the standardized test statistic:

\text{Standardized test statistic} : \frac{\text{statistic}-\text{parameter}}{\text{standard error of the statistic}}

For this problem we are looking at the slope variable.

\text{Standardized test statisitc} = \frac{b-\beta}{s_b}

The null hypothesis is that the slope of the population is 0. The statistic and standard error for the sample statistic is given in the computer output.

\text{Standardized test statisitc} = \frac{-2.20-0}{0.07}