C compare the confidence interval you calculated innbsp

Question

Refer to Exercise 9.58.

a. Using no information about x, estimate and calculate a 95% confidence interval for the mean value of y.

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

c. Compare the confidence interval you calculated in  parts c and d of exercise 9.58 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: ß₁ = 0 against H_a; ß₁ ≠ 0. Use α = .05.

Exercise 9.58

Consider the pairs of measurements shown in the next table.

a. Construct a scattergram for these data.

b. Plot the least Squares line on your scattergram.

c. Use a 95% confidence interval to estimate the mean value of y when x_ρ = 6. Plot the upper and lower bounds of the interval on your scattergram.

d. Repeat part c for x_ρ = 3.2 and x_ρ = 0.

e. Compare the widths of the three confidence intervals your constructed in parts c and d and explain why they differ.