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 before itsintroduction into the market. A typical test performed is the following: The weights of a random sample of fivepeople are recorded before they are introduced to the liquid protein diet. The five individuals are theninstructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) areagain recorded. The results are listed in the table. Let μ1 be the true mean weight of individuals before startingthe diet and let μ2 be the true mean weight of individuals after 3 weeks on the diet. Calculate a 90% confidenceinterval for the difference between the mean weights before and after the diet is used. Assume that the paireddata came from a population that is normally distributed. $$\begin{array}{l}\begin{array} { c c c } \text { Person } & \text { Weight Before Diet } & \text { Weight After Diet } \\1 & 152 & 145 \\2 & 197 & 192 \\3 & 190 & 187 \\4 & 199 & 193 \\5 & 206 & 202\end{array}\\\text { Summary information is as follows: } \overline { \mathrm { d } } = 5 , \mathrm {~s} \mathrm {~d} = 1.58 \text {. }\end{array}$$