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. x 67 64 75 86 73 73 y 42 40 48 51 44 51 (a) Verify that Σx = 438, Σy = 276, Σx2 = 32264, Σy2 = 12806, Σxy = 20295, and r ≈ 0.823. Σx Σy Σx2 Σy2 Σxy r (b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. (c) Verify that Se ≈ 2.9785, a ≈ 8.997, b ≈ 0.5069, and x ≈ 73.000. Se a b x (d) Find the predicted percentage of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.) %(e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.) lower limit % upper limit % (f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that β > 0.Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0.Fail to reject the null hypothesis, there is sufficient evidence that β > 0. (g) Find a 90% confidence interval for β. (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 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.

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. x 67 64 75 86 73 73 y 42 40 48 51 44 51 (a) Verify that Σx = 438, Σy = 276, Σx2 = 32264, Σy2 = 12806, Σxy = 20295, and r ≈ 0.823. Σx Σy Σx2 Σy2 Σxy r (b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. (c) Verify that Se ≈ 2.9785, a ≈ 8.997, b ≈ 0.5069, and x ≈ 73.000. Se a b x (d) Find the predicted percentage of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.) %(e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.) lower limit % upper limit % (f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that β > 0.Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0.Fail to reject the null hypothesis, there is sufficient evidence that β > 0. (g) Find a 90% confidence interval for β. (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 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.

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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Concept explainers

Question

x	67	64	75	86	73	73
y	42	40	48	51	44	51

(a) Verify that Σx = 438, Σy = 276, Σx² = 32264, Σy² = 12806, Σxy = 20295, and r ≈ 0.823.

Σx
Σy
Σx²
Σy²
Σxy
r

(b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.)

t
critical t

Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ > 0.Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.

S_e
a
b
x

(d) Find the predicted percentage of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.)
%

(e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.)

lower limit	%
upper limit	%

(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

t
critical t

Conclusion

Reject the null hypothesis, there is sufficient evidence that β > 0.Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0.Fail to reject the null hypothesis, there is sufficient evidence that β > 0.

(g) Find a 90% confidence interval for β. (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 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.

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