Answer each question completely, showing all your work.

A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person%u2019s 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).

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

Mean hours of exercise per week: 3+14+14+14+3+5+10+11+8+7+6+11+6+11+8+15+8+8+10+5 =177/20= 8.85

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

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

d. 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.

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

Participant Hours of Exercise Life Satisfaction 14 14 4 4 14 4 5 3 10 5 10 3 11 4 10 4 11 12 11 5 13 14 11 10 15 4 16 15 17 4 18 5 19 10 4 20 5