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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please assist with incorrect and unanswered areas in this problem
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.
х | 0.324
0.340
0.276
8.0
0.248
0.367
0.269
y
2.6
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
Ex2 .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 null hypothesis, there is sufficient evidence that p differs from 0.
(c) Verify that S, 1.9184, a z 25.998, and b= -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 y %
(e) Find a 95% confidence interval for y when x = 0.32. (Use 2 decimal places.)
lower limit -561
upper limit 10.947
(f) Use a 1% level of significance to test the claim that B+ 0. (Use 2 decimal places.)
critical t + 3.747
Conclusion
Reject the null hypothesis, there is sufficient evidence that ß differs from 0.
Reject the null hypothesis, there is insufficient evidence that ß 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 ß differs from 0.
(g) Find a 95% confidence interval for ß and interpret its meaning. (Use 2 decimal places.)
lower limit
upper limit
Interpretation
For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside
the confidence interval.
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.
Transcribed Image Text: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. х | 0.324 0.340 0.276 8.0 0.248 0.367 0.269 y 2.6 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 Ex2 .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 null hypothesis, there is sufficient evidence that p differs from 0. (c) Verify that S, 1.9184, a z 25.998, and b= -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 y % (e) Find a 95% confidence interval for y when x = 0.32. (Use 2 decimal places.) lower limit -561 upper limit 10.947 (f) Use a 1% level of significance to test the claim that B+ 0. (Use 2 decimal places.) critical t + 3.747 Conclusion Reject the null hypothesis, there is sufficient evidence that ß differs from 0. Reject the null hypothesis, there is insufficient evidence that ß 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 ß differs from 0. (g) Find a 95% confidence interval for ß and interpret its meaning. (Use 2 decimal places.) lower limit upper limit Interpretation For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval. 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.
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