Refer to Exercise 11.85.

a. Using no information about x, estimate and calculate a 95% confidence interval for the mean value of y. [Hint: Use the one-sample t methodology of Section 5.4.]

b. Plot the estimated mean value and the confidence interval as horizontal lines on your scatterplot.

c. Compare the confidence intervals you calculated in parts c and d of Exercise 11.77 with the one you calculated in part a of this exercise. Does x appear to contribute information about the mean value of y?

d. Check the answer you gave in part c with a statistical test of the null hypothesis H0: b1 = 0 against Ha: b1 ≠ 0. Use a = .05.