Question

Section 9.2 Questions #7-8

9.2: Comparing Popular Diets Because about two-thirds of Americans are considered overweight, weight loss is big business. There are many different types of diets, but do some work better than others? Is low fat better than low carb or is some combination best? Researchers conducted a study involving four popular diets: Atkins (very low carb), Zone (40:30:30 ratio of carbs, protein, fat), LEARN (high carbohydrate, low fat), and Ornish (low fat). They randomly assigned women aged 25-50 with a body mass index (BMI) of 27-40 (overweight and obese) to one of the three diets. The 311 women who volunteered for the program were educated on their assigned diet and were observed periodically as they stayed on the diet for a year. At the end of the year, the researchers calculated the change in BMI (e.g., negative means reduction in BMI) for each woman and compared the results across the four diets.

Answer 1

7.

Atkins

The parameter of interest in this situation is μA that is mean Atkin diet and μW that is mean body mass index of women.

The null hypothesis is that there is a relationship between the popular diets and BMI.

The null hypothesis is that there is no a relationship between the mean bone mineral density of the heavy smokers and light smokers.

H0:μA=μW

H1:μA≠μW

Zone

The parameter of interest in this situation is μZ that is mean Zone diet and μW that is mean body mass index of women.

The null hypothesis is that there is a relationship between the popular diets and BMI.

The null hypothesis is that there is no a relationship between the mean bone mineral density of the heavy smokers and light smokers.

H0:μZ=μW

H1:μZ≠μW

Learn

The parameter of interest in this situation is μL that is mean Learn diet and μW that is mean body mass index of women.

The null hypothesis is that there is a relationship between the popular diets and BMI.

The null hypothesis is that there is no a relationship between the mean bone mineral density of the heavy smokers and light smokers.

H0:μL=μW

H1:μL≠μW

Ornish

The parameter of interest in this situation is μO that is mean Ornish diet and μW that is mean body mass index of women.

The null hypothesis is that there is a relationship between the popular diets and BMI.

The null hypothesis is that there is no a relationship between the mean bone mineral density of the heavy smokers and light smokers.

H0:μO=μW

H1:μO≠μW

8. In the above case the explanatory variable (independent variable) has four categories to gauge the impact on the dependent variable which is BMI. The possible pairwise comparison for each independent variable-dependent variable is three, whereas for all the data set the possible pairwise comparison are twelve.