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 exercising program, both in kinds of exercises and in 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 appropriate decision is ______.

A) fail to reject the null hypothesis that the three groups have different levels of depression
B) reject the null hypothesis that the three groups have different levels of depression
C) fail to reject the null hypothesis that the three groups have equal levels of depression
D) reject the null hypothesis that the three groups have equal levels of depression
E) fail to reject the null hypothesis that the sample is random