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A New Weight-Reducing Technique, Consisting of a Liquid Protein Diet μ1\mu _ { 1 }

Question 79

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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\mu _ { 1 } be the true mean weight of individuals before starting the diet and let μ2\mu _ { 2 } be the true mean weight of individuals after 3 weeks on the diet.

Person Weight Before Diet Weight After Diet
11461392191186318418141931875200196\begin{array} { l l l } 1 & 146 & 139 \\ 2 & 191 & 186 \\ 3 & 184 & 181 \\ 4 & 193 & 187 \\ 5 & 200 & 196 \end{array}

Summary information is as follows: dˉ=5,sd=1.58\bar { d } = 5 , s _ { d } = 1.58 .
Test to determine if the diet is effective at reducing weight. Use α=.10\alpha = .10 .

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