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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. 0.312 0.300 0.340 4.0 0.248 8.6 0.367 3.1 0.269 у 3.4 7.5 11.1 (a) Verify that Ex = 1.836, Ey = 37.7, Ex2 = 0.571498, Ey2 = 290.59, Exy = 10.9272, and r= -0.845.

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. 0.312 0.300 0.340 4.0 0.248 8.6 0.367 3.1 0.269 у 3.4 7.5 11.1 (a) Verify that Ex = 1.836, Ey = 37.7, Ex2 = 0.571498, Ey2 = 290.59, Exy = 10.9272, and r= -0.845.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. х 0.312 y 3.4 0.300 7.5 0.340 0.248 0.367 3.1 0.269 4.0 8.6 11.1 (a) Verify that Ex = 1.836, Ey = 37.7, Ex2 = 0.571498, Ey2 = 290.59, Exy = 10.9272, andr= -0.845. Ex 1.836 Ey 37.7 Ex2 0.571498 Ey2 290.59 Exy 10.9272 r -0.845 (b) Use a 5% level of significance to test the claim that p + 0. (Use 2 decimal places.) t -3.16 critical t + 2.776 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, 1.9623, a = 25.531, and b -62.900. Se 1.9623 a 25.531 b -62.900 (d) Find the predicted percentage ŷ of strikeouts for a player with an x = 0.312 batting average. (Use 2 decimal places.) | % (e) Find a 90% confidence interval for y when x = 0.312. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 5% 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 ß differs from 0. O Reject the null hypothesis, there is insufficient evidence that ß 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 ß differs from 0. (g) Find a 90% confidence interval for ß 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 within the confidence interval. O For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval. 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 average, the percentage strikeouts increases by an amount that falls outside the confidence interval.
Transcribed Image Text: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. х 0.312 y 3.4 0.300 7.5 0.340 0.248 0.367 3.1 0.269 4.0 8.6 11.1 (a) Verify that Ex = 1.836, Ey = 37.7, Ex2 = 0.571498, Ey2 = 290.59, Exy = 10.9272, andr= -0.845. Ex 1.836 Ey 37.7 Ex2 0.571498 Ey2 290.59 Exy 10.9272 r -0.845 (b) Use a 5% level of significance to test the claim that p + 0. (Use 2 decimal places.) t -3.16 critical t + 2.776 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, 1.9623, a = 25.531, and b -62.900. Se 1.9623 a 25.531 b -62.900 (d) Find the predicted percentage ŷ of strikeouts for a player with an x = 0.312 batting average. (Use 2 decimal places.) | % (e) Find a 90% confidence interval for y when x = 0.312. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 5% 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 ß differs from 0. O Reject the null hypothesis, there is insufficient evidence that ß 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 ß differs from 0. (g) Find a 90% confidence interval for ß 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 within the confidence interval. O For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval. 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 average, the percentage strikeouts increases by an amount that falls outside the confidence interval.
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