# ANOVA, Chi-square

8.To examine the effect of pets in stressful situations researchers recruited 45 women who said they were dog lovers. Fifteen of the subjects were randomly assigned to each of the 3 groups to do a stressful task alone with a good friend present, or with their dog present. (The stressful task was to count backwards by 13s or 17s). The subjects mean heart rate during the task is one measure of the effect of stress. The Minitab ANOVA output for the data is given below.

MINITAB

Analysis of Variance for rate

Source DF SS MS F P

group 2 2387.7 1193.8 14.08 0.000

Error 42 3561.3 84.8

Total 44 5949.0

Level N Mean StDev

control 15 82.524 9.242

friend 15 91.325 9.970

pet 15 73.483 9.970

Pooled StDev = 9.208

a)Do the mean heart rates for the groups appear to show that the prescence of a pet or a friend reduce heart rate during a stressful task?

b) What are the values of the ANOVA F-Statistic and its P-value? What hypothesis does F test? Briefly describe the conclusions you draw from these data. Did you find anything surprising?

9. Are the smoking habits of teenagers related to their parents' smoking? Below are the results of a survey of teenagers in eight Arizona high schools. Expected values are in parenthesis. Perform a hypothesis test to determine if the smoking habits of teenagers are independent of the smoking habits of their parents. Test at the 0.05 level of significance.

Teenager

smokes doesn't smoke total

Parents

Both Smoke 400(332.49) 1380(1447.51) 1780

only one smokes 416(418.22) 1823(1820.78) 2239

Niether smokes 188(253.29) 1168(1102.71) 1356

https://brainmass.com/statistics/chi-squared-test/anova-chi-square-4349

#### Solution Preview

8.To examine the effect of pets in stressful situations researchers recruited 45 women who said they were dog lovers. Fifteen of the subjects were randomly assigned to each of the 3 groups to do a stressful task alone with a good friend present, or with their dog present. (The stressful task was to count backwards by 13s or 17s). The subjects mean heart rate during the task is one measure of the effect of stress.

The Minitab ANOVA output for the data is given below.

MINITAB

Analysis of Variance for rate

Source DF SS MS F P

group 2 2387.7 1193.8 14.08 0.000

Error 42 3561.3 84.8

Total 44 5949.0

Level N Mean StDev

control 15 82.524 9.242

friend 15 91.325 9.970

pet 15 73.483 9.970

Pooled StDev ...

#### Solution Summary

Answers to 2 questions on testing hypothesis using ANOVA and Chi-squared test

1) ANOVA: Given a MINITAB ANOVA output, the hypothesis that the prescence of a pet or a friend reduce heart rate during a stressful task.

2) Chi-square test: The hypothesis that the smoking habits of teenagers is related to their parents' smoking is tested using Chi-square test of independence.