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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) Column1 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count -5 0.707107 -5 #N/A 1.581139 2.5 -1.2 0 4 -7 -3 -25 5 Use Excel, we get the above table, we know that the sample mean of the differences is Xd=-5. b. Find Sd (the sample standard deviation of the differences) Use Excel, we get the above table in part a) , we know that the sample standard deviation of the differences is Sd=1.581139 c. Test to determine if the diet is effective at reducing weight. Use alpha= .10. t-Test: Paired Two Sample for Means Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Variable 1 186.8 455.7 5 0.998443 Variable 2 181.8 499.7 5 0 4 7.071068 0.001055 2.131847 0.002111 2.776445 Use Excel, we get the above table. From the table, we know that the pvalue=0.001055<0.10, so we should reject the null hypothesis. We conclude that the diet is effective at reducing weight.