Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 11.33 (p. 601). The data were used to fit the simple linear regression model, E(y) = β0 + β1x, where y = ideal partner's height (in inches) and x = student's height (in inches). One model was fitted for male students and one model was fitted for female students. Consider a student who is 66 inches tall.
a. If the student is a female, use the model to predict the height of her ideal mate. Form a 95% confidence interval for the prediction and interpret the result.
b. If the student is a male, use the model to predict the height of his ideal mate. Form a 95% confidence interval for the prediction and interpret the result.
c. Which of the two inferences, parts a and b, may be invalid? Why?