The appropriate test to compare means from multiple groups (in this case, three populations) while assuming normality and equal variances among groups is the Analysis of Variance (ANOVA) test is can safely employ ANOVA the correct answer b.
Certainly! When testing the null hypothesis that the means of three or more populations are equal with unknown but assumed equal variances, the Analysis of Variance (ANOVA) is the preferred statistical test. ANOVA evaluates whether there are significant differences among the means of multiple groups simultaneously.
It determines if any variations in the sample data are due to actual differences in population means or are simply the result of random variability. Using three separate t-tests for each pairwise comparison might yield higher chances of making a Type I error (false-positive) due to multiple testing.
ANOVA avoids this issue by considering all groups simultaneously, making it a more powerful and efficient method for assessing differences in means. It tests the null hypothesis by comparing the variance between group means against the variance within groups, providing a reliable indication of whether at least one group mean significantly differs from the others.