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

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. $$\begin{array}{l}\begin{array} { c c c } \text { Person } & \text { Weight Before Diet } & \text { Weight After Diet } \\1 & 163 & 156 \\2 & 208 & 203 \\3 & 201 & 198 \\4 & 210 & 204 \\5 & 217 & 213\end{array}\\\text { Summary information is as follows: } \bar { d } = 5 , s d = 1.58 \text {. }\end{array}$$ Calculate a 90% confidence interval for the difference between the mean weights before
and after the diet is used.