A Researcher Wants to Study the Effects of Physical Exercise

Multiple Choice

A researcher wants to study the effects of physical exercise on depression.She randomly selects a group of 24 individuals who are equally depressed.None of these individuals currently exercises.She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group) , group 2 exercises once a week, and group 3 exercises two times a week.Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercise program (kinds of exercises and intensity) .After two months, the researcher has all individuals take a depression-assessment test.The score of the test goes from 0 = totally miserable to 100 = complete satisfaction. The scores are shown in the following table:
$$\begin{array} { | c c c | } \hline \text { Group 1 } & \text { Group 2 } & \text { Group } 3 \\\hline 25 & 24 & 35 \\15 & 16 & 22 \\20 & 19 & 31 \\17 & 24 & 32 \\23 & 25 & 31 \\21 & 25 & 29 \\19 & 21 & 33 \\18 & 18 & 35 \\\hline\end{array}$$ The researcher uses a Kruskal-Wallis test and a significance level $\alpha$ = 0.05.The sum of the ranks for group 3, T_3, is ______.

A) 157
B) 158
C) 159
D) 160
E) 161