V 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 146 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 = 39.11 +5.51x. The standard error of the slope of this least-squares regression line was approximately 2.27. 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 Bj. (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 complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis #1- B P Ho : D H1 : 0 (b) Determine the type of test statistic to use. Choose one) V (c) Find the value of the test statistic. (Round to three or more decimal places.) X (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) and (e) 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