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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 0.344 0.308 0 0.248 0.367 0.269 y 2.6 7.6 4.0 11.1 (a) Verify that Ex = 1.876, Ey = 37, Ex? = 0.597354, Ey2 = 287.3, Exy = 10.8516, and /~ -0.898. Ex Ev EV2 Exv (b) Use a 10% level of significance to test the claim that p # 0. (Use 2 decimal places.) critical t + Conclusion O Reject the null hypothesis, there is sufficient evidence that p differs from 0. O Reject the null hypothesis, there is insufficient evidence that p differs from 0. O Fail to reject the null hypothesis, there is insufficient evidence that p differs from 0. O Fail to reject the null hypothesis, there is sufficient evidence that p differs from 0. (c) Verify that S. ~ 1.6945, a & 26.943, and b & -66.448. (d) Find the predicted percentage y of strikeouts for a player with an x = 0.286 batting average. (Use 2 decimal places.) (e) Find a 99% confidence interval for y when x = 0.286. (Use 2 decimal places.) lower limit upper limit (f) Use a 10% level of significance to test the claim that B = 0. (Use 2 decimal places.) critical t + Conclusion O Reject the null hypothesis, there is sufficient evidence that B differs from 0. O Reject the null hypothesis, there is insufficient evidence that B differs from 0. O Fail to reject the null hypothesis, there is insufficient evidence that B differs from 0. O Fail to reject the null hypothesis, there is sufficient evidence that B differs from 0. (g) Find a 99% confidence interval for $ and interpret its meaning. (Use 2 decimal places.) lower limit upper limit Interpretation O For every unit increase in batting average, the percentage strikeouts increases by an amount that falls outside the confidence interval. O For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval. O For every unit increase in batting average, the percentage strikeouts increases by an amount that falls within the confidence interval. For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls within the confidence interval