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Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n= 6 professional basketball players gave the following information. x67 64 75 86 73 73 42 39 48 51 44 51 (a) Verify that Ex = 438, Ey = 275, Ex? = 32264, Ey² = 12727, Exy = 20231, and r= 0.827. Ex 438 Ey 275 Ex2 32264 Ey2 12727 Exy 20231

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n= 6 professional basketball players gave the following information. x67 64 75 86 73 73 42 39 48 51 44 51 (a) Verify that Ex = 438, Ey = 275, Ex? = 32264, Ey² = 12727, Exy = 20231, and r= 0.827. Ex 438 Ey 275 Ex2 32264 Ey2 12727 Exy 20231

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 percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. х | 67 y 64 86 73 51 44 75 73 42 39 48 51 (a) Verify that Ex = 438, Ey = 275, Ex? = 32264, Ey? = 12727, Exy = 20231, and r= 0.827. %3D Ex 438 Σy 275 Ex2 32264 Ey2 12727 Exy 20231 0.827 (b) Use a 5% level of significance to test the claim that p> 0. (Round your answers to two decimal places.) t 2.942 critical t 2.132 Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is sufficient evidence that p> 0. (c) Verify that S, 3.1191, a = 6.564, b = 0.5379, and x = 73.000. s, 3.119 a 6.564 b 0.5379 x 73 (d) Find the predicted percentage ŷ of successful field goals for a player with x = 71% successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval for y when x = 71. (Round your answers to one decimal place.) lower limit % % upper limit (f) Use a 5% level of significance to test the claim that 6 > 0. (Round your answers to two decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ß > 0. O Reject the null hypothesis, there is insufficient evidence that ß > 0. O Fail to reject the null hypothesis, there is insufficient evidence that B > 0. O Fail to reject the null hypothesis, there is sufficient evidence that ß > 0. (9) Find a 90% confidence interval for ß. (Round your answers to three decimal places.) lower limit upper limit Interpret its meaning. O For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval. O For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval. O For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval. O For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval.
Transcribed Image Text:Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. х | 67 y 64 86 73 51 44 75 73 42 39 48 51 (a) Verify that Ex = 438, Ey = 275, Ex? = 32264, Ey? = 12727, Exy = 20231, and r= 0.827. %3D Ex 438 Σy 275 Ex2 32264 Ey2 12727 Exy 20231 0.827 (b) Use a 5% level of significance to test the claim that p> 0. (Round your answers to two decimal places.) t 2.942 critical t 2.132 Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is sufficient evidence that p> 0. (c) Verify that S, 3.1191, a = 6.564, b = 0.5379, and x = 73.000. s, 3.119 a 6.564 b 0.5379 x 73 (d) Find the predicted percentage ŷ of successful field goals for a player with x = 71% successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval for y when x = 71. (Round your answers to one decimal place.) lower limit % % upper limit (f) Use a 5% level of significance to test the claim that 6 > 0. (Round your answers to two decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ß > 0. O Reject the null hypothesis, there is insufficient evidence that ß > 0. O Fail to reject the null hypothesis, there is insufficient evidence that B > 0. O Fail to reject the null hypothesis, there is sufficient evidence that ß > 0. (9) Find a 90% confidence interval for ß. (Round your answers to three decimal places.) lower limit upper limit Interpret its meaning. O For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval. O For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval. O For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval. O For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval.
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