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

Parts (a) and (b) relate to testing p. Part (c) requests the value of Se. Part (e) relates to confidence intervals for prediction. Part (f) relates to testing β.
Answers may vary due to rounding.
(a) Verify that ˆ‘x = 1.842, ˆ‘y = 37.6, ˆ‘x2 = 0.575838, ˆ‘y2 = 290.78, ˆ‘xy = 10.87, and r ‰ˆ ˆ’0.891.
(b) Use a 5% level of significance to test the claim that r 2 0.
(c) Verify that Se ‰ˆ 1.6838, a ‰ˆ 26.247, and b ‰ˆ 265.081.
(d) Find the predicted percentage of strikeouts for a player with an x = 0.300 batting average.
(e) Find an 80% confidence interval for y when x = 0.300.
(f) Use a 5% level of significance to test the claim that β ‰  0.

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