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 44 41 48 51 44 51 (a) verify that σx = 438, σy = 279, σx2 = 32264, σy2 = 13059, σxy = 20493, and r ≈ 0.800. σx correct: your answer is correct. σy correct: your answer is correct. σx2 correct: your answer is correct. σy2 correct: your answer is correct. σxy correct: your answer is correct. r correct: your answer is correct. (b) use a 5% level of significance to test the claim that rho > 0. (round your answers to two decimal places.) t correct: your answer is correct. critical t incorrect: your answer is incorrect. conclusion reject the null hypothesis, there is sufficient evidence that rho > 0. reject the null hypothesis, there is insufficient evidence that rho > 0. fail to reject the null hypothesis, there is insufficient evidence that rho > 0. fail to reject the null hypothesis, there is sufficient evidence that rho > 0. (c) verify that se ≈ 2.7729, a ≈ 14.783, b ≈ 0.4345, and x ≈ 73.000. se correct: your answer is correct. a correct: your answer is correct. b correct: your answer is correct. x correct: your answer is correct. (d) find the predicted percentage y hat 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 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.