Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.324 y 2.6 0.276 0.340 0.248 0.367 0.269 8.0 4.0 8.6 3.1 11.1 (a) Verify that Ex = 1.824, Ey = 37.4, Ex = 0.565306, Ey = 293.54, Exy = 10.6668, and rs -0.870. Ex 1.824 Ey 37.4 Ex? 565306 Ey2 293.54 Exy 10.6668 r -870 (b) Use a 1% level of significance to test the claim that p + 0. (Use 2 decimal places.) critical t+ 3.747 Conclusion O Reject the null hypothesis, there is sufficient evidence that p differs from 0. O Reject the null hypothesis, there is insufficient evidence that p differs from 0. O Fail to reject the null hypothesis, there is insufficient evidence that p differs from 0. O Fail to reject the nul hypothesis, there is sufficient evidence that p differs from 0. (c) Verify that S= 1.9184, a = 25.998, and bs -65.014. S. 1.9184 a 25.998 b -65.014 (d) Find the predicted percentage ŷ of strikeouts for a player with an x = 0.32 batting average. (Use 2 decimal places.) 5.193 % (e) Find a 95% confidence interval for y when x = 0.32. (Use 2 decimal places.) lower limit -561 upper limit 10.947 v % (F) Use a 1% level of significance to test the claim that 6 + 0. (Use 2 decimal places.) critical t+ 3.747 Conclusion O Reject the null hypothesis, there is sufficient evidence that ß differs from 0. Reject the null hypothesis, there is insufficient evidence that B differs from 0. Fail to reject the null hypothesis, there is insufficient evidence that ß differs from 0. Fail to reject the null hypothesis, there is sufficient evidence that 6 differs from 0. (9) Find a 95% confidence interval for ß and interpret its meaning. (Use 2 decimal places.) lower limit upper limit Interpretation O For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval. O For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls within the confidence interval. O For every unit increase in batting average, the percentage strikeouts increases by an amount that falls within the confidence interval. O For every unit increase in batting average, the percentage strikeouts increases by an amount that falls outside the confidence interval.