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

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: $$\begin{array} { c | c | c } \text { Customer } & \text { Initial } & \text { One Year } \\\hline 1 & 185 & 175 \\2 & 192 & 193 \\3 & 125 & 115 \\4 & 148 & 146 \\5 & 165 & 170 \\6 & 220 & 175 \\7 & 265 & 170 \\8 & 177 & 174 \\9 & 302 & 266 \\10 & 112 & 116 \\11 & 154 & 148 \\12 & 230 & 256\end{array}$$ What alternative hypothesis should be tested in order to determine if the diet is successful at helping customers lose and keep weight off after one year?

A) The distribution of initial weight is identical to the distribution of one-year weight.
B) The distribution of initial weight is shifted to the right of the distribution of one-year weight.
C) The distribution of initial weight is shifted to the left of the distribution of one-year weight.
D) The distribution of initial weight is shifted to the right or to the left of the distribution of one-year weight.