The correct equation for the F ratio in ANOVA is F= MSb / MSw, which compares the variance between group means to the variance within the groups. This ratio follows an F distribution, which is used to determine if the means of several populations are significantly different.
In ANOVA, the formula for the F ratio is F = MSb / MSw, where MSb stands for Mean Squares Between groups and MSw stands for Mean Squares Within groups. This equation represents option 2) F= MSb / MSw from the student's list. The F ratio helps determine if the group means are significantly different by comparing the variance between the group means to the variance within the groups.
ANOVA assumptions include that each population from which a sample is taken is normally distributed, all populations have equal standard deviations, and the samples are randomly and independently selected from the populations. The ANOVA test is right-tailed; a high F statistic corresponds to a low p-value, potentially leading to the rejection of the null hypothesis. Furthermore, the calculation of the F ratio involves dividing the sum of squares by their respective degrees of freedom (df) to find the mean squares.
The answer to the student's question about the equation for F in ANOVA is F= MSb / MSw. This statistic, which follows an F distribution, is crucial for conducting a one-way ANOVA hypothesis test to determine if there are differences among population means.