Use the formula information. When testing the slope M of the regression line for the population, you usually test that the slope is 0, or Ho: M = 0. A slope of 0 indicates that there is no linear relationship between x and y. To perform the t-test for the slope M, use the standardized test statistic with n - 2 degrees of freedom.
Then, using the critical values found in Table 5 in Appendix B, make a decision whether to reject or fail to reject the null hypothesis. You can also use the LinRegTTest feature on a TI-83/84 Plus to calculate the standardized test statistic as well as the corresponding P-value. If P ≤ α, then reject the null hypothesis. If P > α, then do not reject Ho.
The following table shows the ages (in years) and salaries (in thousands of dollars) of a random sample of engineers at a company. Test the claim of M ≠ 0. Use α = 0.05. Then interpret the results in the context of the problem. If convenient, use technology to solve the problem.