Chapter 9.3, Problem 8P

In Problems 7–12, parts (a) and (b) relate to testing ρ. Part (c) requests the value of S_e. Parts (d) and (e) relate to confidence intervals for prediction. Parts (f) and (g) relate to testing β and finding confidence intervals for β.

Answers may vary due to rounding.

8. 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 = 6 professional baseball players gave the following information (Reference: The Baseball Encyclopedia, Macmillan).

1. (a) Verify that ∑x = 1.842, ∑y = 37.6, ∑x² = 0.575838, ∑y² = 290.78, ∑xy = 10.87, and $r\approx 0.891$.
2. (b) Use a 5% level of significance to test the claim that $\rho \ne 0$.
3. (c) Verify that $S_e\approx 1.6838$, $a\approx 26.247$, and $b\approx -65.081$.
4. (d) Find the predicted percentage of strikeouts for a player with an x = 0.300 batting average.
5. (e) Find an 80% confidence interval for y when x = 0.300.
6. (f) Use a 5% level of significance to test the claim that $\beta \ne 0$.
7. (g) Find a 90% confidence interval for β and interpret its meaning.