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 0.332 0.276 0.340 0.248 0.367 0.269 y 2.8 7.3 4.0 8.6 3.1 11.1 (a) Verify that Σx = 1.832, Σy = 36.9, Σx2 = 0.570554, Σy2 = 283.91, Σxy = 10.5608, and r ≈ -0.884. 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 Se ≈ 1.7611, a ≈ 25.426, and b ≈ -63.130. Se a b (d) Find the predicted percentage y hat of strikeouts for a player with an x = 0.336 batting average. (Use 2 decimal places.) % (e) Find a 99% confidence interval for y when x = 0.336. (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 99% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit

Answer 1