Exercise 6.27 introduces data from a random sample of 170 married couples in Britain, where both partners' ages are below 65 years, and fits a model predicting wife's age from husband's age. Wife's age has a mean of 40.68 years, with standard deviation 11.41 years. Husband's age has a mean of 42.92 years, with standard deviation 11.76 years. From software, the residual standard error is \(s=3.95\).

(a) Use the summary statistics to calculate a \(95 \%\) confidence interval for the average age of wives whose husbands are 55 years old.

(b) You meet a married man from Britain who is 55 years old. Predict his wife's age and give a \(95 \%\) prediction interval for her age.

(c) Repeat parts (a) and (b) using the approximate formulas for the appropriate standard errors.

Data From Exercise 6.27

6.27 Husbands and wives, Part II. Exercise 6.25 presents a scatterplot displaying the relationship between husbands' and wives' ages in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Given below is summary output of the least squares fit for predicting wife's age from husband's age. Wife's age (in years) 20- 60- 20 40 Husband's age (in years) 60 (Intercept) age_husband Estimate 1.5740 0.9112 Std. Error: 1.1501 0.0259 t value Pr(>|t) 1.37 35.25 0.1730 0.0000 df = 168