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. 75 86 73 73 48 51 44 x67 64 42 39 (a) Verify that Ex = 438, Ey = 275, Ex² = 32264, Ey? = 12727, Exy = 20231, and r = 0.827. Ex Ex2 Ey2 Exy (b) Use a 5% level of significance to test the claim that p > 0. (Round your answers to two decimal places.) critical t 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. Se a b (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 > 0. (Round your answers to two decimal places.) critical t Conclusion O Reject the null hypothesis, there is sufficient evidence that > 0. O Reject the null hypothesis, there is insufficient evidence that > 0. O Fail to reject the null hypothesis, there is insufficient evidence that > 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.