Hypothesis tests for the correlation coefficient V Espanol 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 148 Coastal State graduates from the last five years was selected, and it was found that the sample correlation coefficient between cumulative grade point average and annual income was 0.12. 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 correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) 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 H1. B P Ho : D H :D (b) Determine the type of test statistic to use. It Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) X 5 2 (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