Here we study the effectiveness of two dieting methods. Method 1 is a diet high
ID: 3371145 • Letter: H
Question
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: 9.01 < ? < 9.99
Method 2: 6.35 < ? < 9.45
(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 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? (Circle One)
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
Ans:
a)Method 1
99% confidence intervals for the mean weight loss
9.01 < ? < 9.99
Sample mean weight loss=(9.99+9.01)/2=9.5 pounds
b)Method 2
99% confidence intervals for the mean weight loss
6.35 < ? < 9.45
Sample mean weight loss=(6.35+9.45)/2=7.9 pounds
c)No, because the confidence intervals overlap.