A dietician developed a diet that is low in fats carbohydrat

A dietician developed a diet that is low in fats, carbohydrates and cholesterol (Diet A). Two random samples of 50 obese people each were selected and one group of 50 was placed on Diet A. The other 50 were placed on a diet that contained approximately the same quantity of food, but was not as low in fats, carbohydrates and cholesterol (Diet B). The amount of weight loss in a 3-week period was recorded. The average weight loss for Diet A was 9.3 pounds. The average weight loss for Diet B was 7.4 pounds. The standard deviation of weight loss for Diet A was 4.7 pounds. The standard deviation of weight loss for Diet B was 4.0 pounds.

(b) Would you expect 0 to be in your confidence interval? Why or why not?

Solution

Two random samples of 50 obese people each were selected one group of 50 was placed on Diet A. The other 50 were placed on a diet that contained approximately the same quantity of food, but was not as low in fats, carbohydrates and cholesterol (Diet B).

The average weight loss for Diet A was 9.3 pounds.

The average weight loss for Diet B was 7.4 pounds.

The standard deviation of weight loss for Diet A was 4.7 pounds.

The standard deviation of weight loss for Diet B was 4.0 pounds.

95% Confidence interval is:

(-)1.96*

===4.36

==0.2

=[(9.3-7.41.96*4.36*0.2]

=[1.91.71]

=[0.19,3.61]

95% confidence includes zero means that there is a small, but statistically meaningful difference in the means. We do not have sufficient evidence to conclude that there is a difference.