Use the data in Exercise 20 in Section 13.1 for the following.

a. Compute a point estimate of the mean height of sons whose fathers are 70 inches tall.

b. Construct a 95% confidence interval for the mean height of sons whose fathers are 70 inches tall.

c. Predict the height of a particular son whose father is 70 inches tall.

d. Construct a 95% prediction interval for the height of a particular son whose father is 70 inches tall.

Exercise 20

In 1906, the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 16 pairs, with height measured in inches, simulated from the distribution specified by Pearson.

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Father's Son's height height Father's Son's height height 70.8 69.8 72.4 69.1 65.4 66.0 65.7 65.3 65.7 70.9 69.1 71.8 69.0 69.1 70.7 71.0 73.6 74.9 72.3 71.9 66.7 68.8 73.6 76.5 70.1 73.3 69.3 71.4 68.3 68.3 64.5 68.5