Question

Over the past year, the vice president of human resources at a large medical center conducted a series of three-month workshops aimed at increasing worker motivation and performance. As a check of effectiveness, she selected 7 employees from the personnel files and recorded their most recent annual performance ratings along with the ratings attained prior to attending the workshops. At a 5% level of significance, is there evidence that the workshops increased performance ratings? Take the differences = before - after.

Before    After
59            72
72            74
89            62
67            74
81            78
88            92
71            81

Take the differences = before-after. Order the data smallest to largest, ignoring the negative signs. Rank the data from 1 to 7.

Observation 5 had the values Before = 81 and After = 78. What is the difference before - after of these values? ____________.

What rank will observation 5 receive?_______.

Add up all the ranks that have a negative difference, T_. What is the value of T_? _________.


Add up all the ranks that have a positive difference, T+. What is the value of T+? __________.


What is the test statistic, T? The minimum(T_,T+)? __________.

From the Table of Critical Values for the Wilcoxon Matched Pairs Signed Rank Test, what is the critical value for the test?

_______________.

Answer 1

Before	after	difference	absolute difference	rank
59	72	-13	13	6
72	74	-2	2	1
89	62	27	27	7
67	74	-7	7	4
81	78	3	3	2
88	92	-4	4	3
71	81	-10	10	5

ranks are based on absolute difference. Observation 5 is ranked 2nd.

T_ = sum of ranks of negative differences = 6+1+4+3+5=19

T+= sum of ranks of positive differences= 7+3=10

test statistic T= smaller of ( T_ and T+) =10

H0 : before=after

H1: before < average

Wcritical value for one tailed test = 3

test statistic > 3

therefore we do not reject null hypothesis