A New Weight-Reducing Technique, Consisting of a Liquid Protein Diet $\mu _ { 1 }$

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 $\mu _ { 1 }$ 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.


$\begin{array}{ccc}\text { Person } & \text { Weight Before Diet } & \text { Weight After Diet } \\1 & 149 & 142 \\2 & 194 & 189 \\3 & 187 & 184 \\4 & 196 & 190 \\5 & 203 & 199\end{array}$

Summary information is as follows: $\bar { d } = 5 , s _ { d } = 1.58$ .

Test to determine if the diet is effective at reducing weight. Use $\alpha = .10$ .