In: Statistics and Probability
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 Se ≈ 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 |