A researcher is interested to learn if there is a linear relationship between the hours in a week...

Question

A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest).

Participant	Hours of Exercise	Life Satisfaction
1	3	1
2	14	2
3	14	4
4	14	4
5	3	10
6	5	5
7	10	3
8	11	4
9	8	8
10	7	4
11	6	9
12	11	5
13	6	4
14	11	10
15	8	4
16	15	7
17	8	4
18	8	5
19	10	4
20	5	4

Find the mean hours of exercise per week by the participants.

Find the variance of the hours of exercise per week by the participants.

Determine if there is a linear relationship between the hours of exercise per week and the life satisfaction by using the correlation coefficient.

Describe the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction.

Develop a model of the linear relationship using the regression line formula.

Insomnia has become an epidemic in the United States. Much research has been done in the development of new pharmaceuticals to aide those who suffer from insomnia. Alternatives to the pharmaceuticals are being sought by sufferers. A new relaxation technique has been tested to see if it is effective in treating the disorder. Sixty insomnia sufferers between the ages of 18 to 40 with no underlying health conditions volunteered to participate in a clinical trial. They were randomly assigned to either receive the relaxation treatment or a proven pharmaceutical treatment. Thirty were assigned to each group. The amount of time it took each of them to fall asleep was measured and recorded. The data is shown below. Use the appropriate
t-test to determine if the relaxation treatment is more effective than the pharmaceutical treatment at a level of significance of 0.05.

Relaxation	Pharmaceutical
98	20
117	35
51	130
28	83
65	157
107	138
88	49
90	142
105	157
73	39
44	46

005_az21a5o-1fw12vgd.docx

Robert · Accepted Answer

1.  
a. . 
Statistics 
Hours of Exercise 
N 
Valid 20 
Missing 0 
Mean 8.85 
Mean = 8.85
b. . 
Statistics 
Hours of Exercise 
N 
Valid 20 
Missing 0 
Variance 13.397 
Variance   = 13.397
c. . 
Correlations 
 Hours of 
Exercise 
Life Satisfaction 
Hours of Exercise 
Pearson Correlation 1 -.103 
Sig. (2-tailed)  .664 
N 20 20 
Life Satisfaction 
Pearson Correlation -.103 1 
Sig. (2-tailed) .664  
N 20 20
There is a weak negative linear correlation, r = -0.103
d. Amount of variation in the life satisfaction ranking that is due to the relationship 
between the hours of exercise per week and the life satisfaction. 
Model Summary 
Model R R Square Adjusted R 
Square 
Std. Error of the 
Estimate 
1 .103
a
 .011 -.044 2.535 
a. Predictors: (Constant), Hours of Exercise 
R Square  =  0.011  = 1.1% 
1.1% variation in Life Satisfaction ranking is due to the relationship between the hours 
of exercise per week and the life satisfaction. 
e. . 
Coefficients
a
 
Model Unstandardized Coefficients Standardized 
Coefficients 
t Sig. 
B Std. Error Beta 
1 
(Constant) 5.671 1.516  3.740 .001 
Hours of Exercise -.070 .159 -.103 -.441 .664 
a. Dependent Variable: Life Satisfaction 
The general equation for simple linear regression is: 
Y = b0 + b1X 
The model  
LifeS  = 5.671 – 0.70HrsEx 
Where LifeS represents Life Satisfaction and HrsEx is the Hours of Exercise. 
2.

A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a...

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