4. (Based on Stock & Watson Introduction to Econoes" 6th ed., Exercise 5.8.) Suppose that (Y, X) satisfy the simple linear regression assumptions. In addition, u is N (0, σ.) and is independent of Xi. A sample of size n = 30 yields : = 43.2+61.5X,, n = 30, R2 = 0.54. (10.2) (7.4) (a) Construct a 95% confidence interval for (b) Test H0 : β1-55 v.s. Hi : β1 55 at the significance level 5%. (c) Test H0 : β1-55 v.s. Hi : β.> 55 at the 5% level. 4. (Based on Stock & Watson Introduction to Econoes" 6th ed., Exercise 5.8.) Suppose that (Y, X) satisfy the simple linear regression assumptions. In addition, u is N (0, σ.) and is independent of Xi. A sample of size n = 30 yields : = 43.2+61.5X,, n = 30, R2 = 0.54. (10.2) (7.4) (a) Construct a 95% confidence interval for (b) Test H0 : β1-55 v.s. Hi : β1 55 at the significance level 5%. (c) Test H0 : β1-55 v.s. Hi : β.> 55 at the 5% level.