3. -5 points An exercise science major wants to try to use body weight to predic

Question

3. -5 points An exercise science major wants to try to use body weight to predict how much someone can bench press. He collects the data shown below on 30 male students. Both quantities are measured in pounds. Assignment 10g3 data a) What type of association does there appear to be between these two variables? no association negative association can not be determined O positive association b) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the lower limit? Give your answer to two decimal places. c) Compute a 95% confidence interval for the average bench press of 150 pound males. What is the upper limit? Give your answer to two decimal places. d) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the lower limit? Give your answer to two decimal places. e) Compute a 95% prediction interval for the bench press of a 150 pound male. What is the upper limit? Give your answer to two decimal places.

Explanation / Answer

Part a

The correlation coefficient between the given two variables is given as 0.831792, which means there is strong positive linear association or relationship exists between two variables.

Answer:

Positive association

Part b

Here, we have to find the lower limit for 95% confidence interval for bench press.

Confidence interval = Xbar -/+ t*SD/sqrt(n)

Lower limit = = Xbar - t*SD/sqrt(n)

Sample size = n = 30

Degrees of freedom = 30 – 1 = 29

Confidence level = 95%

Critical t value = 2.0452

Xbar = 141.07

SD = 15.18

Lower limit = 141.07 - 2.0452*15.18/sqrt(30) = 135.40

Part c

Here, we have to find the upper limit for 95% confidence interval for bench press.

Confidence interval = Xbar -/+ t*SD/sqrt(n)

Upper limit = = Xbar + t*SD/sqrt(n)

Sample size = n = 30

Degrees of freedom = 30 – 1 = 29

Confidence level = 95%

Critical t value = 2.0452

Xbar = 141.07

SD = 15.18

Upper limit = 141.07 + 2.0452*15.18/sqrt(30) = 146.73

Part d

Here, we have to find the prediction interval for the dependent variable bench press which is summarized as below:

Confidence Interval Estimate

Data

X Value

150

Confidence Level

95%

Intermediate Calculations

Sample Size

30

Degrees of Freedom

28

t Value

2.048407

XBar, Sample Mean of X

164.4333

Sum of Squared Differences from XBar

19931.37

Standard Error of the Estimate

8.574951

h Statistic

0.043785

Predicted Y (YHat)

134.1154

For Average Y

Interval Half Width

3.6755

Confidence Interval Lower Limit

130.4400

Confidence Interval Upper Limit

137.7909

For Individual Response Y

Interval Half Width

17.9454

Prediction Interval Lower Limit

116.1700

Prediction Interval Upper Limit

152.0609

Confidence Interval Estimate

Data

X Value

150

Confidence Level

95%

Intermediate Calculations

Sample Size

30

Degrees of Freedom

28

t Value

2.048407

XBar, Sample Mean of X

164.4333

Sum of Squared Differences from XBar

19931.37

Standard Error of the Estimate

8.574951

h Statistic

0.043785

Predicted Y (YHat)

134.1154

For Average Y

Interval Half Width

3.6755

Confidence Interval Lower Limit

130.4400

Confidence Interval Upper Limit

137.7909

For Individual Response Y

Interval Half Width

17.9454

Prediction Interval Lower Limit

116.1700

Prediction Interval Upper Limit

152.0609

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