Question

Coastal State University is conducting a study regarding the possible relationship between the cumulative grade point average and the annual income of its recent graduates.

A random sample of 151 Coastal State graduates from the last five years was selected, and it was found that the least-squares regression equation relating cumulative grade point average (denoted by x, on a 4-point scale) and annual income (denoted by y, in thousands of dollars) was y hat=40.37+5.50x. The standard error of the slope of this least-squares regression line was approximately 4.04.

Test for a significant linear relationship between grade point average and annual income for the recent graduates of Coastal State by doing a hypothesis test regarding the population slope β1.(Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and perform a two-tailed test. Then fill in the table below.

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	Z/ T/ CHI SQ / F
The value of the test statistic: (Round to at least three decimal places.)
The two critical values at the 0.05 level of significance: (Round to at least three decimal places.)
Based on the data, can the university conclude (using the 0.05 level) that there is a significant linear relationship between grade point average and annual income for its recent graduates?

Answer 1

Conclusion: The university cannot conclude (using the 0.05 level) that there is a significant linear relationship between grade point average and annual income for its recent graduates.