Question

question 6 options: suppose that a one-way anova is being performed to compare the means of 4 populations and that the sample sizes are 15, 17, 20, and 14. determine the degrees of freedom for the f-statistic. (a) the degree of freedom of the numerator (enter as an integer) (b) the degree of freedom of the denominator (enter as an integer)

Answer 1

In a one-way ANOVA with four populations, the degrees of freedom for the numerator is 3 and for the denominator is 62.

Step-by-step explanation:

To determine the degrees of freedom for the F-statistic in a one-way ANOVA:

1. The degree of freedom of the numerator (dfbetween) is one less than the number of groups. Since there are 4 populations, the dfbetween is 4 - 1 which is 3.
2. The degree of freedom of the denominator (dfwithin) is the total number of samples across all groups minus the number of groups. The total sample size is 15 + 17 + 20 + 14 which equals 66. Thus, the dfwithin = 66 - 4 which is 62.

Therefore, the degrees of freedom for the numerator is 3 and for the denominator is 62.