# Perform a two-way analysis of variance and explain the results

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

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

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.

2.      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 53 194 20 94 50 95 92 161 112 154 71 75 96 57 86 34 92 118 75 41 41 145 102 148 24 117 96 177 108 119 102 186 35 22 46 61 74 75

3.      A researcher is interested to learn if there is a relationship between the level of interaction a women in her 20s has with her mother and her life satisfaction ranking. Below is a list of women who fit into each of four level of interaction. Conduct a One-Way ANOVA on the data to determine if a relationship exists.

 No Interaction Low Interaction Moderate Interaction High Interaction 2 3 3 9 4 3 10 10 4 5 2 8 4 1 1 5 7 2 2 8 8 2 3 4 1 7 10 9 1 8 8 4 8 6 4 1 4 5 3 8

4.      Is there a relationship between handedness and gender? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05.

 Left-Handed Right-Handed Men 13 22 Women 27 18

5.      A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

 Diet Exercise <30% fat 30% – 60% fat >60% fat <60 minutes 4 3 2 4 1 2 2 2 2 4 2 2 3 3 1 60 minutes 6 8 5 or more 5 8 7 4 7 5 4 8 5 5 6 6

a.       Perform a two-way analysis of variance and explain the results. (Show all work to receive full credit)

b.      Find the effect size for each factor and the interaction and explain the results. (Show all work to receive full credit)