Do reducing diets work? Dr. Linda Stern and her colleagues recruited $132$obese adults at the Philadelphia Veterans Affairs Medical Center in Pennsylvania. Half of the participants were randomly assigned to a low-carbohydrate diet and the other half were assigned to a low-fat diet. Researchers measured each participant’s change in weight and cholesterol level after six months and again after one year. Subjects in the low-carb diet group lost significantly more weight than subjects in the low-fat diet group during the first six months of the study. At the end of a year, however, the average weight loss for subjects in the two groups was not significantly different.

(a) Why did researchers randomly assign the subjects to the diet treatments?

(b) Explain to someone who knows little statistics what “lost significantly more weight” means.

(c) The subjects in the low-carb diet group lost an aver-age of $5.1$kg in a year. The subjects in the low-fat diet group lost an average of $3.1$kg. Explain how this infor-

mation could be consistent with the fact that weight loss in the two groups was not significantly different.

$132$participants were assigned diets randomly to obtain results for weight loss.

An experiment was conducted in which half participant was given low carbohydrate diet and half were given low fat diet. to examine change in weight and cholesterol. The participant in low carb diet lost an average of$5.1$ kg and subjects in low fat diet lost an average of$3.1$kg.

An experiment was conducted in which half participant was given low carbohydrate diet and half were given low fat diet. to examine change in weight and cholesterol. The researchers randomly assign the subjects as randomization is one of the three principles of experimental design. It is also done to make sure that different groups are as similar as possible.

As the context of above experiment, “lost significantly more weight” means the difference in weight loss is large that cannot be due to chance and cannot be ignored.

As per the results, the participant in low carb diet lost an average of $5.1$kg and subjects in low fat diet lost an average of $3.1$kg.

The total difference in weight loss was $2$kg that appeared over a period of an year. This could be due to chance. Hence weight loss is not statistically significant.