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    ANOVA, Chi-square

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    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

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    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.

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