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

Multiple Choice

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: $\begin{array}{c|c|c}\text { Customer } & \text { Initial } & \text { One Year } \\\hline 1 & 185 & 175 \\2 & 192 & 193 \\3 & 125 & 115 \\4 & 148 & 146 \\5 & 165 & 170 \\6 & 220 & 175 \\7 & 265 & 170 \\8 & 177 & 174 \\9 & 302 & 266 \\10 & 112 & 116 \\11 & 154 & 148 \\12 & 230 & 256\end{array}$

Calculate the test statistic 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.

A) $\mathrm { T } _ { + } = 78$
B) $\mathrm { T } _ { + } = 59$
C) $\mathrm { T } _ { - } = 19$
D) $\mathrm { T } _ { + } = 26$