MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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. 67 64 75 86 73 73 y 44 41 48 51 44 51 (a) Verify that Ex = 438, Ey = 279, Ex2 = 32264, Ey2 = 13059, Exy = 20493, and rs 0.800. Ex 438 Ey 279 Ex2 32264 Ey2 13059 Exy 20493 r.800 (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 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, 2.7729, a s 14.783, b = 0.4345, and x= 73.000. S 2.7729 a 14.783 b 0.4345 x 73 (d) Find the predicted percentage ŷ of successful field goals for a player with x = 77% successful free throws. (Round your answer to two decimal places.) 48.238 % (e) Find a 90% confidence interval for y when x = 77. (Round your answers to one decimal place.) lower limit 41.852 % upper limit 54.624 % (f) Use a 5% level of significance to test the claim that B> 0. (Round your answers to two decimal places.) critical t 2.132 Conclusion Reject the null hypothesis, there is sufficient evidence that 6 > 0. Reject the null hypothesis, there is insufficient evidence that ß > 0. O Fail to reject the null hypothesis, there is insufficient evidence that ß > 0. 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. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval. 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.
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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. 67 64 75 86 73 73 y 44 41 48 51 44 51 (a) Verify that Ex = 438, Ey = 279, Ex2 = 32264, Ey2 = 13059, Exy = 20493, and rs 0.800. Ex 438 Ey 279 Ex2 32264 Ey2 13059 Exy 20493 r.800 (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 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, 2.7729, a s 14.783, b = 0.4345, and x= 73.000. S 2.7729 a 14.783 b 0.4345 x 73 (d) Find the predicted percentage ŷ of successful field goals for a player with x = 77% successful free throws. (Round your answer to two decimal places.) 48.238 % (e) Find a 90% confidence interval for y when x = 77. (Round your answers to one decimal place.) lower limit 41.852 % upper limit 54.624 % (f) Use a 5% level of significance to test the claim that B> 0. (Round your answers to two decimal places.) critical t 2.132 Conclusion Reject the null hypothesis, there is sufficient evidence that 6 > 0. Reject the null hypothesis, there is insufficient evidence that ß > 0. O Fail to reject the null hypothesis, there is insufficient evidence that ß > 0. 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. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval. 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.
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