Answer :
Final answer:
The correct answer for the degrees of freedom for the F statistic is (b) 2 and 96. The numerator degree of freedom is 2 (k - 1 where k is the number of groups), and the denominator degree of freedom is 96 (n - k where n is the total sample size).
Explanation:
The question pertains to the determination of the degrees of freedom (df) for the F statistic, which is a component of ANOVA tests used to compare the variances between groups. To determine the degrees of freedom for the F statistic, we need two values: the df for the numerator (between groups) and the df for the denominator (within groups).
From the information given, we can infer that the F statistic was calculated for a scenario with 3 groups (k = 3), since one of the df values is mentioned as 2 (which would be k - 1). We also know that the total sample size across all groups is 100 (n = 100), as one option mentions df values adding up to 96 or 97, which suggests a total of 98 or 99 degrees of freedom for the within-group variance (total n minus k).
The correct answer is hence (b) 2 and 96, since the df for the numerator would be 2 (k - 1 = 3 - 1) and the df for the denominator would be 96 (n - k = 100 - 3), assuming each group has an equal number of members.
Additionally, it is worth noting that since the null hypothesis of overall equality of population means is rejected at the 5% significance level, this implies that the obtained F value exceeded the critical F value for the corresponding degrees of freedom.
