An exercise science major wants to try to use body weight to

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.

Body weight,Bench press
147, 139
127, 139
154, 129
209, 155
201, 169
153, 135
188, 155
174, 163
139, 126
129, 115
167, 143
142, 124
185, 160
161, 147
217, 161
133, 110
180, 148
213, 159
134, 119
135, 128
184, 155
168, 159
209, 157
132, 139
121, 122
179, 158
204, 162
137, 126
148, 142
131, 139

a) What type of association does there appear to be between these two variables?

no association

can not be determined

negative association

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.  

Solution

a) What type of association does there appear to be between these two variables?

no association

can not be determined   

negative association

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.  

132.92 pounds

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.  

140.17 pounds

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.

118.12 pounds

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.

154.98 pounds

Regression Analysis

r²

0.722

n

30

r

0.850

k

1

Std. Error

8.822

Dep. Var.

Bench press

ANOVA table

Source

SS

df

MS

F

p-value

Regression

5,654.1863

1  

5,654.1863

72.65

2.89E-09

Residual

2,179.1804

28  

77.8279

Total

7,833.3667

29  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=28)

p-value

95% lower

95% upper

Intercept

66.7451

9.0633

7.364

5.10E-08

48.1797

85.3105

Body weight

0.4653

0.0546

8.523

2.89E-09

0.3535

0.5772

Predicted values for: Bench press

95% Confidence Interval

95% Prediction Interval

Body weight

Predicted

lower

upper

lower

upper

Leverage

150

136.547

132.924

140.169

118.116

154.977

0.040

Regression Analysis
	r²	0.722	n	30
	r	0.850	k	1
	Std. Error	8.822	Dep. Var.	Bench press
ANOVA table
Source	SS	df	MS	F	p-value
Regression	5,654.1863	1	5,654.1863	72.65	2.89E-09
Residual	2,179.1804	28	77.8279
Total	7,833.3667	29
Regression output				confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	66.7451	9.0633	7.364	5.10E-08	48.1797	85.3105
Body weight	0.4653	0.0546	8.523	2.89E-09	0.3535	0.5772
Predicted values for: Bench press
		95% Confidence Interval	95% Prediction Interval
Body weight	Predicted	lower	upper	lower	upper	Leverage
150	136.547	132.924	140.169	118.116	154.977	0.040