The professor of an introductory statistics course has found something interesting: there may be a relationship between scores on his first midterm and the number of years the test-takers have spent...

Question #31 please just find (a) because what I put is wrong


Extracted text: The professor of an introductory statistics course has found something interesting: there may be a relationship between scores on his first midterm and the number of years the test-takers have spent at the university. For the 59 students taking the course, the professor found that the least-squares regression equation relating the two variables number of years spent by the student at the university (denoted by x) and score on the first midterm (denoted by y) is = 78.97 – 2.57x. The standard error of the slope of the least-squares regression line is approximately 1.66. Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B1. (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 H and the alternative hypothesis H,. H, : B = 0 H, : B # 0 OSO (b) Determine the type of test statistic to use. O20 Degrees of freedom: 57 (c) Find the value of the test statistic. (Round to three or more decimal places.) - 1.5482 unlue (Round to three or more decimal places.)