Question

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.

x	0.318	0.280	0.340	0.248	0.367	0.269
y	3.2	7.2	4.0	8.6	3.1	11.1

(a) Verify that Σx = 1.822, Σy = 37.2, Σx² = 0.563678, Σy² = 284.86, Σxy = 10.65, and r ≈ -0.861.

Σx
Σy
Σx2
Σy2
Σxy
r

(b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.)

t
critical t ±

(c) Verify that S_e ≈ 1.8731, a ≈ 25.079, and b ≈ -62.170.

Se
a
b

(d) Find the predicted percentage  of strikeouts for a player with an x = 0.346 batting average. (Use 2 decimal places.)
%

(e) Find a 90% confidence interval for y when x = 0.346. (Use 2 decimal places.)

lower limit	%
upper limit	%

(f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.)

t
critical t ±

(g) Find a 90% confidence interval for β and interpret its meaning. (Use 2 decimal places.)

lower limit
upper limit

Answer 1