Problem #36 Hypothesis Testing for Slope:
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 â‰¤ Î±, then reject the
null hypothesis. If P > Î±, 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 â‰ 0.
Use Î± = 0.05. Then interpret the results in the context of the problem. If
convenient, use technology to solve the problem.