Question

As part of an investigation of the long-term impact of diet on cardiovascular disease, total cholesterol levels (in nmol/l) were measured for subjects who had adhered to one of the four different dietary lifestyles for a period of at least one year: vegan (no milk or meat products), vegetarian (milk, but no meat), fish (fish and milk, but no other meat), and meat (unrestricted). The results are presented below. Assume that total cholesterol level is normally distributed within each group, and that the population standard deviations are all equal. Diet group Mean SD Sample Size 4.4 0.8 10 Vegan Vegetarian 4,9 0.8 11 Fish 5.0 0.9 12 Meat 5.5 0.9 12 Calculate the within-groups variance for these four populations. Provide the answer below in the text box (round answer to the second decimal place). You do not have to upload your work.

Answer 1

Within Group Variations is given by the equation

SUM[(n - 1) * SD²] = (9 * 0.8²) + (10 * 0.8²) + (11 * 0.9²) + (11 * 0.9²) = 5.76 + 6.4 + 8.91 + 8.91 = 29.98

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The within group variation tells us the amount of variation between each sample within each group. The sum of these gives us the total variation within the groups.