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:   8.61 < μ < 9.59
Method 2:   6.19 < μ < 9.01

(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?

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)

99% CI for Method 1 = 8.61 < μ < 9.59

Range of the confidence interval is given as = 9.59 - 8.61 = 0.98. Half width of the interval is given as = 0.98/2 = 0.49

Therefore, the mean is given as 8.61 + 0.49 = 9.1

The sample mean weight loss for participants in the Method 1 diet plan 9.1

(b)

99% CI for Method 2 = 6.19 < μ < 9.01

Range of the confidence interval is given as = 9.01 - 6.19 = 2.82. Half width of the interval is given as = 2.82/2 = 1.41. Therefore, the mean is given as 6.19 + 1.41 = 7.6

The sample mean weight loss for participants in the Method 2 diet plan 7.6

(c)

No, because the confidence intervals overlap.