Basketball: Free Throws and Field Goals Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season.

A random sample of n 5 6 professional basketball players gave the following information (Reference:

The Official NBA Basketball Encyclopedia, Villard Books).

x 67 65 75 86 73 73 y 44 42 48 51 44 51

(a) Verify that Sx 5 439, Sy 5 280, Sx2 5 32,393, Sy2 513,142, Sxy 5 20,599, and r < 0.784.

(b) Use a 5% level of significance to test the claim that r . 0.

(c) Verify that Se < 2.6964, a < 16.542, b < 0.4117, and x < 73.167.

(d) Find the predicted percentage yˆ of successful field goals for a player with x 5 70% successful free throws.

(e) Find a 90% confidence interval for y when x 5 70.

(f) Use a 5% level of significance to test the claim that b . 0.

(g) Find a 90% confidence interval for b and interpret its meaning.

parts

(a) and

(b) relate to testing r. Part (c)
requests the value of Se. Parts

(d) and

(e) relate to confidence intervals for prediction. Parts

(f) and (g) relate to testing b and finding confidence intervals for b .AppendixLO1