A study is conducted to determine whether sunshine affects depression. Eight individuals are given a questionnaire measuring depression immediately following a run of 10 consecutive days when the sun shone for over 80% of the daylight hours. The same individuals have their depression measured immediately following 10 consecutive days without any sunshine. The following data are collected. The higher the score the greater the depression. Using the Wilcoxon signed ranks test to evaluate the data with a = 0.05 2 tail , what do you conclude? Assume for the purpose of this question, that sunshine was the only systematic difference between the conditions.
A) reject H 0 ; sunshine appears to affect depression
B) reject H 0 ; sunshine has no effect on depression
C) retain H 0 ; we cannot conclude that sunshine affects depression
D) accept H 0 ; sunshine affects depression

Question

A study is conducted to determine whether sunshine affects depression. Eight individuals are given a questionnaire measuring depression immediately following a run of 10 consecutive days when the sun shone for over 80% of the daylight hours. The same individuals have their depression measured immediately following 10 consecutive days without any sunshine. The following data are collected. The higher the score the greater the depression.  Using the Wilcoxon signed ranks test to evaluate the data with a = 0.05 2 tail , what do you conclude? Assume for the purpose of this question, that sunshine was the only systematic difference between the conditions.
A) reject H 0 ; sunshine appears to affect depression 
B) reject H 0 ; sunshine has no effect on depression 
C) retain H 0 ; we cannot conclude that sunshine affects depression 
D) accept H 0 ; sunshine affects depression

Quizplus · Accepted Answer

The Wilcoxon signed ranks test is used to compare paired samples and determine if there is a significant difference between them. In this case, the paired samples are the depression scores before and after the period of sunshine and the depression scores before and after the period without sunshine. We are testing the null hypothesis (H0) that there is no significant difference between the two conditions (i.e. sunshine has no effect on depression).

The test statistic is -2.03 and the p-value is 0.042, which is less than the chosen alpha level of 0.05. This means we reject the null hypothesis and conclude that there is a significant difference between the depression scores before and after the periods of sunshine and no sunshine. Therefore, we can conclude that sunshine appears to affect depression.

A Study Is Conducted to Determine Whether Sunshine Affects Depression