10. [-/5.34 Points] DETAILS BBUNDERSTAT12 9.3.008. MY NOTES ASK YOUR TEACHER 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 0.338 0.292 0.340 0.248 0.367 0.269 y 3.4 7.6 4.0 8.6 3.1 11.1 (a) Verify that Ex = 1.854, Zy = 37.8, Ex2 = 0.583662, Zy = 292.1, Exy = 10.9848, and r = -0.912. 5 / 2 Exy (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. Reject the null hypothesis, there is insufficient evidence that p differs from 0. Fail to reject the null hypothesis, there is insufficient evidence that p differs from 0. Fail to reject the null hypothesis, there is sufficient evidence that p differs from 0. (c) Verify that S = 1.5070, a = 26.240, and b = -64.532. (d) Find the predicted percentage y of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.) % (e) Find a 99% confidence interval for y when x = 0.288. (Use 2 decimal places.) lower limit % upper limit |% (f) Use a 10% level of significance to test the claim that / # 0. (Use 2 decimal places.) critical t # Conclusion O Reject the null hypothesis, there is sufficient evidence that / differs from 0. O Reject the null hypothesis, there is insufficient evidence that / 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. (9) 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 within the confidence interval. O For every unit increase in batting aver age, the creases 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