A New Weight-Reducing Technique, Consisting of a Liquid Protein Diet

Essay

A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. 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 μ1 be the true mean weight of individuals before starting the diet and let μ2 be the true mean weight of individuals after 3 weeks on the diet. $\begin{array}{ccc}\text { Person } & \text { Weight Before Diet } & \text { Weight After Diet } \\1 & 166 & 159 \\2 & 211 & 206 \\3 & 204 & 201 \\4 & 213 & 207 \\5 & 220 & 216\end{array}$

Summary information is as follows: $\bar { d } = 5 , s _ { d } = 1.58$ . Calculate a 90% confidence interval for the difference between the mean weights before and after the diet is used.