Question 10.51

10.51 Two confidence intervals.

The data used for Exercise 10.47 include 195 men 30 years old. The mean income of these men is and the standard deviation of these 195 incomes is .

  1. Use the one-sample procedure to give a 95% confidence interval for the mean income of 30-year-old men.
  2. Why is this interval different from the 95% confidence interval for in the regression output?

(Hint: What data are used by each method?)

10.51

(a) (44,446, 55,314). (b) The interval from part (a) only includes information from the 195 30-year-old men, while the interval for the mean response in the output uses the data from all 5712 men to give a better estimate for the 30-year-olds.