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=36.86+5.50x . The standard error of the slope of this least-squares regression line was approximately 2.17.

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.

(If necessary, consult a list of formulas.)

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one) 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.) _____ and_____ 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? Yes No

Answer 1

Ho:

H1:

Type of test statistic: t; Degrees of freedom = 151 - 2 = 149

Test statistic = 5.50/2.17 = 2.535

Two critical values: -1.976 and 1.976

Conclusion: Yes