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Inferences Based on Two Samples

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. A typical test performed by the FDA is the following: 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.

Person Weight before diet Weight after diet
1 150 143
2 195 190
3 188 185
4 204 200
5 197 191

a. Find XD (the sample mean of the differences)

b. Find SD (the sample standard deviation of the differences)

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

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