Tractor rollover protection. Refer to the Human Factors (February 2020) study on the incorrect usage of foldable rollover protection structures (FROPS) for tractors, Exercises 11.23 (p. 659) and 11.55 (p. 673). Consider, again, the simple linear regression model relating FROPS pivot pin-top distance (y) to farmer’s working experience (x).

a. You used the estimated model to predict the pivot pintop distance set by a farmer with 25 years of experience. Find and interpret a 99% prediction interval for this distance.

b. Now, find and interpret a 99% prediction interval for the pivot pin-top distance set by a farmer with 10 years of experience.

c. Explain why the interval, part

a, is narrower than the interval, part

b. d. Find and interpret a 99% confidence interval for the mean pivot pin-top distance set by all farmers with 10 years of experience.

e. Explain why the interval, part

a, is wider than the interval, part d.