Question

A study of the effects of smoking on sleeping classifies subjects as nonsmokers, moderate smokers, or heavy smokers. The investigators interview a sample of 200 people in each group. Assume all the conditions are met. The degrees of freedom for the ANOVA F test statistic comparing the mean hours of sleep are:

OPTION 1: A. 2 and 197
OPTION 2: B. 2 and 597
OPTION 3: C. 3 and 597
OPTION 4: D. 597 and 2

Answer 1

The degrees of freedom for the ANOVA F test statistic comparing the mean hours of sleep among different smoker classifications are 2 for the numerator and 597 for the denominator, which corresponds to OPTION 2: B.

Step-by-step explanation:

The student asked about the degrees of freedom for the ANOVA F test statistic when comparing the mean hours of sleep for nonsmokers, moderate smokers, or heavy smokers, with 200 people in each group. In ANOVA, the degrees of freedom for the numerator are calculated as the number of groups minus one, and for the denominator, it's the total number of observations minus the number of groups.

In this case, we have three groups, so the numerator degrees of freedom will be 3 - 1 = 2. Since there are 200 people in each of the three groups, the total number of observations is 600. Thus, the denominator degrees of freedom is 600 - 3 = 597. Therefore, the degrees of freedom for the F test statistic are 2 and 597, which corresponds to OPTION 2: B.