Question

One-factor ANOVA for independent samples is used to evaluate the mean differences in BMI (i.e., body mass index) of three groups of adults - young adults, middle age adults and elderly. Each age group had n = 21 participants. If the computed F = 3.78, which of the following is the correct conclusion from this study (use p <. 05 for your test)?

A. Reject the null hypothesis and conclude that there are some significant differences in mean BMI.

B. Fail to reject the null hypothesis and conclude that there are some significant differences in mean BMI.

C. Reject the null hypothesis and conclude that there are no significant differences in mean BMI.

D. Fail to reject the null hypothesis and conclude that there are no significant differences in mean BMI.

Answer 1

The correct option is (A), i.e., Reject the null hypothesis and conclude that there are some significant differences in mean BMI.

We have given that there are 3 groups (young adults, middle age adults, elderly) and each having participants. Also the F-statistic is given in the question as F=3.78. It is also given that the p-value is less than , i.e.,

Now,

The null and alternative hypothesis for one way anova is given as :

Sicne based on the sample data the null hypothesis is rejected than according to alternative hypothesis we conclude that, "at least one of the groups true mean BMI is different than others." Or we can say that there is a significant difference in mean BMI.