Diet Methods: Here we study the effectiveness of two dieting methods. Method 1 i

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 95% confidence intervals for the mean weight loss of each plan are given below.

Method 1:   8.23 < < 9.17
Method 2:   6.74 < < 7.86

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

x1 =  pounds

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

x2 =  pounds

(c) Are you 95% 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.

Explanation / Answer

a. Here for method 1, CI is Method 1:   8.23 < < 9.17

So UCL=mean+E=9.17

& LCL = mean-E=8.23

Solving this we get 2mean=17.4

So mean=8.7

b. Method 2:   6.74 < < 7.86

As we did in a, mean=7.3

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

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