Baseball: Batting Average and Strikeouts Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n 5 6 professional baseball players gave the following information (Reference: The Baseball Encyclopedia, Macmillan).

x 0.328 0.290 0.340 0.248 0.367 0.269 y 3.2 7.6 4.0 8.6 3.1 11.1

(a) Verify that Sx 51.842, Sy 5 37.6, Sx2 5 0.575838, Sy2 5 290.78, Sxy 510.87, and r < 20.891.

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

(c) Verify that Se < 1.6838, a < 26.247, and b < 265.081.

(d) Find the predicted percentage of strikeouts for a player with an x 5 0.300 batting average.

(e) Find an 80% confidence interval for y when x 5 0.300.

(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