Question

Practitioners measured spiritual well-being (SWB) in a sample of 16 adults who were alcoholic before and following treatment for alcoholism.

Change in SWB Following Treatment
+11	−1
+10	−6
−8	+13
+20	−5
+12	−2
−3	+7
+14	+15
+9	−4

Use the normal approximation for the Wilcoxon signed-ranks T test to analyze the data above. (Round your answer to two decimal places.)
z =  

State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

Answer 1

1. Ranking the differences and affixing a sign to each rank

Rank the dis, ignoring the signs (i.e. assign rank 1 to the smallest |di |, rank 2 to the next etc.)

Label each rank with its sign, according to the sign of di .

d: Change in SWB Following Treatment	rank	Sign
11	11	+
10	10	+
−8	8	-
20	16	+
12	12	+
−3	3	-
14	14	+
9	9	+
−1	1	-
−6	6	-
13	13	+
−5	5	-
−2	2	-
7	7	+
15	15	+
−4	4	-

2. Calculate W+, the sum of the ranks of the positive differences: d's, and W−, the sum of the ranks of the negative differences d's.

d: Change in SWB Following Treatment	rank	Sign
11	11	+
10	10	+
20	16	+
12	12	+
14	14	+
9	9	+
13	13	+
7	7	+
15	15	+
Total	107

W+ = 107

d: Change in SWB Following Treatment	rank	Sign
−8	8	-
−3	3	-
−1	1	-
−6	6	-
−5	5	-
−2	2	-
−4	4	-
Total	29

W- = 29

3. Choose W = min(W−, W+).

W = min (29, 107) = 29

4. Normal approximation :

Z = -2.0166

For two tailed test :

=  0.05

As P-Value i.e. is less than Level of significance i.e (P-value:0.0438 < 0.05:Level of significance); Reject Null Hypothesis

Reject null hypothesis.