Suppose a growing health and wellness company is rolling out three new nutritional diet plans. The research department wants to test the effectiveness of these three new nutritional plans, a low-fat plan and a low-carb plan, as well as its standard low calorie plan. Marcia, a nutrition researcher with the company, randomly assigns 21 new weight loss program participants to each of the three plans, assigning 7 to each plan. After administering the plans, she follows up with the particip As Marcia examines the collected data, she observes that the distribution of weight loss results for each sample are approximately normal without any outliers. As population variances are unknown, Marcia assumes equal variances on the sample data because side -by-side boxplots of the samples indicate relatively equal sizes of the variances. ants a month later and records the amount of weight, in pounds, that each participant lost. ght losses
Marcia intends to conduct a one-way ANOVA F-test at a significance level of α-005 to test if the mean wei for the three diet plans are all equal. The mean square between groups, MSG, is 17 .7733, and the mean square within also referred to as the mean square crror, MSE, is 6.8162. Marcia computes the F-statistic, which is F 2.6075.
Select the statement that accurately evaluates whether or not the requirements of a one-way ANOVA F-test have been met in Marcia's experiment. If the requirements have not been met, do not proceed to answer subsequent questions.
A. The requirements have been met because the sampling distributions are approximately normal and the dependent variable is categorical.
B. The requirements have been met because the samples are properly selected, are approximately normally distributed, and each contains at least 5 observations. The requirements have not been met because the population variances are unknown.
C. The requirements have been met because the samples are properly selected and are approximately normally distributed with equal variances.
D. The requirements have not been met because the sample sizes are not properly selected and are not large enough.