Chapter 4.2, Problem 74E

(a)

To determine

To explain why did the researchers randomly assign the subjects to the diet treatments.

Explanation of Solution

In the question, an experiment was conducted in which the researchers examined each participant’s change in weight and cholesterol level after six months and again after year as the participants were half given the low-carbohydrate diet and half were given the low-fat diet. Thus, the researchers randomly assign the subjects to the diet treatments because randomization is one of the three principles of experimental design and randomization is necessary to make sure that the different groups are as similar as possible.

(b)

To determine

To explain to someone who knows little statistics what “lost significantly more weight” means.

Explanation of Solution

In the question, an experiment was conducted in which the researchers examined each participant’s change in weight and cholesterol level after six months and again after year as the participants were half given the low-carbohydrate diet and half were given the low-fat diet. Thus, in this context, “lost significantly more weight” means that the weight loss difference is so large that the difference cannot be due to chance.

(c)

To determine

To explain how this information could be consistent with the fact that weight loss in the two groups was not significantly different.

Explanation of Solution

In the question, an experiment was conducted in which the researchers examined each participant’s change in weight and cholesterol level after six months and again after year as the participants were half given the low-carbohydrate diet and half were given the low-fat diet. The subjects in the low-crab diet group lost an average of $5.1$ kg in a year. The subjects in the low-fat group diet lost an average of $3.1$ kg. Thus, in total the difference in weight loss was $2$ kg. This weight loss appeared over a period of one year. A weight loss difference of $2$ kg in one year could be due to chance, which then means that the weight loss is not significantly different.