Do Popular Diets Really Help Customers in the Long-Run? Many

Short Answer

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A commercially successful diet company conducted a study of twelve randomly selected customers and measured their weight after before starting the diet and then again after staying with the diet for a year. The company hoped that the initial weight loss would be sustained after the first year on the diet. The data is shown below: $\begin{array}{c|c|c}\text { Customer } & \text { Initial } & \text { One Year } \\\hline 1 & 185 & 175 \\2 & 192 & 193 \\3 & 125 & 115 \\4 & 148 & 146 \\5 & 165 & 170 \\6 & 220 & 175 \\7 & 265 & 170 \\8 & 177 & 174 \\9 & 302 & 266 \\10 & 112 & 116 \\11 & 154 & 148 \\12 & 230 & 256\end{array}$

Find the rejection region for the Wilcoxon Signed Rank Test to test to determine if the distribution of initial weight is shifted to the right of the distribution of one-year weight. Test using $\alpha = 0.05$ .
A) $T _ { - } \leq 14$
B) $T _ { - } \leq 10$
C) $T _ { - } \leq 7$
D) $T _ { - } \leq 17$