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.
$$\begin{array}{l}\begin{array} { c c c } \text { Person } & \text { Weight Before Diet } & \text { Weight After Diet } \\1 & 147 & 140 \\2 & 192 & 187 \\3 & 185 & 182 \\4 & 194 & 188 \\5 & 201 & 197\end{array}\\\text { Summary information is as follows: } \bar { d } = 5 , s _ { d } = 1.58 \text {. }\end{array}$$
Calculate a 90% confidence interval for the difference between the mean weights before and after the diet is used.