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 39 48 51 44 51 (a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.) (b) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.) t = critical t = Conclusion Reject the null hypothesis, there is sufficient evidence that ? > 0. Reject the null hypothesis, there is insufficient evidence that ? > 0. Fail to reject the null hypothesis, there is insufficient evidence that ? > 0. Fail to reject the null hypothesis, there is sufficient evidence that ? > 0. (c) Find Se, a, b, and x. (Round your answers to four decimal places.) (d) Find the predicted percentage ŷ of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.) (e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.) lower limit % upper limit % (f) Use a 5% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.) t = critical t = Conclusion Reject the null hypothesis, there is sufficient evidence that ? > 0. Reject the null hypothesis, there is insufficient evidence that ? > 0. Fail to reject the null hypothesis, there is insufficient evidence that ? > 0. Fail to reject the null hypothesis, there is sufficient evidence that ? > 0.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 30E

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Question

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	39	48	51	44	51

(a) Find Σx, Σy, Σx², Σy², Σxy, and r. (Round r to three decimal places.)

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

t =
critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ? > 0.

Reject the null hypothesis, there is insufficient evidence that ? > 0.

Fail to reject the null hypothesis, there is insufficient evidence that ? > 0.

Fail to reject the null hypothesis, there is sufficient evidence that ? > 0.

(d) Find the predicted percentage ŷ of successful field goals for a player with x = 65% successful free throws. (Round your answer to two decimal places.)

(e) Find a 90% confidence interval for y when x = 65. (Round your answers to one decimal place.)

lower limit	%
upper limit	%

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

t =
critical t =

Conclusion

Reject the null hypothesis, there is sufficient evidence that ? > 0.

Reject the null hypothesis, there is insufficient evidence that ? > 0.

Fail to reject the null hypothesis, there is insufficient evidence that ? > 0.

Fail to reject the null hypothesis, there is sufficient evidence that ? > 0.

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