Construct and Interpret Confidence Intervals About the Population Mean Difference $\mu _ { 1 }$

Short Answer

Construct and Interpret Confidence Intervals about the Population Mean Difference of Matched -Pairs Data
-A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests before its introduction into the market. A typical test performed is the following: The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let $\mu _ { 1 }$ be the true mean weight of individuals before starting the diet and let $\mu _ { 2 }$ be the true mean weight of individuals after 3 weeks on the diet. Calculate a $90 \%$ confidence interval for the difference between the mean weights before and after the diet is used. Assume that the paired data came from a population that is normally distributed.



Summary information is as follows: $\overline { \mathrm { d } } = 5 , \mathrm {~s} \mathrm {~d} = 1.58$ .