Question

Diet Methods: Here we study the effectiveness of two dieting methods. Method 1 is a diet high in protein, fiber, and fat but low in carbohydrates. Method 2 is a diet low in fat but high in fiber and carbohydrates. After one year, a sample of participants from each diet method were checked for the amount of weight lost. The 99% confidence intervals for the mean weight loss of each plan are given below.

Method 1: 8.77 < μ < 9.83
Method 2: 7.38 < μ < 8.42

(a) What is the sample mean weight loss for participants in the Method 1 diet plan? Round your answer to 1 decimal place.

x₁ =

(b) What is the sample mean weight loss for participants in the Method 2 diet plan? Round your answer to 1 decimal place.

x₂ =

(c) Are you 99% confident that the mean weight loss for all those on the Method 1 diet plan is greater than the mean weight loss for all on the Method 2 diet plan and why?

No, because the confidence intervals overlap.

Yes, because upper limit for Method 2 is less than the lower limit for Method 1.    

No, because upper limit for Method 2 is less than the lower limit for Method 1.

Yes, because the confidence intervals overlap.

Answer 1

a) Sample mean weight = (8.77 + 9.83)/2 = 9.3

b) Sample mean weight = (7.38 + 8.42)/2 = 7.9

c) Yes, because upper limit for Method 2 is less than the lower limit for Method 1.