Question

Answer each question completely. Copy and Paste the SPSS output into the word document for the calculations portion of the problems, highlighting correct answers. (Please remember to answer the questions you must interpret the SPSS output).

1. 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

1. Find the mean hours of exercise per week by the participants.
2. Find the variance and standard deviation of the hours of exercise per week by the participants.
3. Run a bivariate correlation to determine if there is a linear relationship between the hours of exercise per week and the life satisfaction. Report the results of the test statistic using correct APA formatting.
4. Run a linear regression on the data. Report the results, using correct APA formatting. Identify 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 (Hint: the R² value)
5. Report a model of the linear relationship between the two variables using the regression line formula.

Answer 1

SOLUTION A: MEAN= 8.85

SOLUTION B: VARIANCE= 13.397 and STANDARD DEVIATION= 3.66

SOLUTION C: NULL HYPOTHESIS H0:

ALERNATIVE HYPOTHESIS Ha:

By using SPSS we have

Correlation r= -0.103

P value= 0.664

Since P value GREATER than 0.05 therefore NOT SIGNIFICANT

Decision: DO NOT REJECT NULL HYPOTHESIS H0.

Conclusion: We do not have sufficient evidence to conclude that there is correlation between Hours of exercise and Life satisfaction.

SOLUTION D:

NULL HPOTHESIS H0:

ALTERNATIVE HYPOTHESIS H0:

Test statistic t= -0.07/0.159= -0.44

P value= 0.664

Since P value >0.05 therefore NOT SIGNIFICANT

Decision: DO NOT REJECT NULL HYPOTHESIS H0.

Conclusion: We do not have sufficient evidence to conclude that there relationship between the hours of exercise per week and the life satisfaction

R squared or coeffcient of determination= 0.011

Interpretation: 1.1% is 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.

e) Model is

where X is the hours of exercise per week