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 y [ 42 64 75 48 51 39 86 73 44 73 51 (a) Verify that Ex = 438, Ey = 275, Ex² = 32264, Ey = 12727, Exy = 20231, andr= 0.827. Ex 438 Ey 275 Ex? 32264 Ey2 12727 Exy 20231 r0.827 (b) Use a 5% level of significance to test the claim that p> 0. (Round your answers to two decimal places.) t2.9420 critical t0.75 x Conclusión Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p> o. Fail to reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject the null hypothesis, there is sufficient evidence that p > 0. (c) Verify that Se ▪ 3.1191, a - 6.564, b - 0.5379, and x - 73.000. Se 3.1191 a 6.564 b0.5379 x x 73.000 (d) Find the predicted percentage ; of successful field goals for a player with x = 67% successful free throws. (Round your answer to two decimal places.) 42.60 (e) Find a 90% confidence interval for y when x = 67. (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 , Reject the null hypothesis, there is sufficient evidence that § > 0. Reject the null hypothesis, there is insufficient evidence that > o. Fail to reject the null hypothesis, there is insufficient evidence that > 0. Fail to reject the null hypothesis, there is sufficient evidence that > 0. (9) Find a 90% confidence interval for 8. (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 within the confidence interval. 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 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.