Consider the estimated equation from Example 4.3, which can be used to study the effects of skipping class on college GPA: (i)Using the standard normal approximation, find the 95% confidence interval for beta_hsGPA' (ii)Can you reject the hypothesis H_0: beta_hsGPA = .4 against the two-sided alternative at the 5% level? (iii) Caii you reject the hypothesis H_0: beta_hsGPA = 1 against the two-sided alternative at the 5% level?
Explanation / Answer
1) CI for slope -> beta +- z(a/2)*SE(beta) lower =0.412-1.96*0.094 0.22776 upper =0.412+1.96*0.094 0.59624 2) ho: beta hrs_GPA = .4 h1: beta hrs_GPA =/= .4 t = (beta-.4)/se_beta t = =(0.412-0.4)/0.094 0.127659574 p-value= =T.DIST.2T(0.12766,139) 0.898603 since p-value >0.05, I fai to reject ho and conclude that beta hrs_GPA = .4 3) ho: beta hrs_GPA = 1 h1: beta hrs_GPA =/= 1 t = (beta-.4)/se_beta t = =(0.412-1)/0.094 -6.255319149 p-value= 4.59097E-09 since p-value < 0.05, I reject ho and conclude that beta hrs_GPA =/= 1