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.

A figure of a computer output is shown. At the top is a table with two rows. The first row reads variable, N, mean, S E mean, and standard deviation. The second row reads running time, 11, 74.81, 2.21, and 7.33. Below this is a second table with three columns labeled predictor, coefficient, and S E coefficient. The first row reads constant, 88.01, and 0.49. The second row reads exercise time, negative 2.20, and 0.07. At the bottom it reads S equals 0.76 and R squared equals 99 percent.

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 ?

Answer 1

The appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 is the t-statistic.

The t-statistic for testing the slope coefficient is calculated as follows:

t = (b1 - 0) / SE(b1)

where b1 is the estimated slope coefficient, and SE(b1) is the standard error of the estimated slope coefficient.

From the computer output, we see that the estimated slope coefficient for exercise time is -2.20, and the standard error of the estimated slope coefficient is 0.07.

Therefore, the t-statistic is:

t = (-2.20 - 0) / 0.07 = -31.43

This t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size. The sample size is not given in the output, so we cannot determine the exact degrees of freedom.