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

question 26

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) $T _ { - } \leq 17$

• A) \(T _ { - } \leq 14\)
• B) \(T _ { - } \leq 10\)
• C) \(T _ { - } \leq 7\)
• D) \(T _ { - } \leq 17\)

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Definitions:

Natural Selection

A fundamental mechanism of evolution, where organisms better adapted to their environment tend to survive and reproduce, passing on advantageous traits.

Joint Evolution

The process by which two or more species evolve in response to each other, influencing each other’s evolutionary pathway.

Binary Influence

A concept that deals with dualistic effects or the impact of two different forces or factors in a given situation.

Genetics

The branch of biology that studies genes, genetic variation, and the inheritance of characteristics in biological organisms.