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, before after. is there evidence that the workshops increased performance ratings?

Take the differences =
Before After
72 59
74 72
62 89
74 67
78 81
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?

Answer 1

Kindly check explanation

Explanation:

Given the data:

Before _After_ diff ___rank

72 ______ 59 __13 __ 2

74 _______ 72 _ 2 __ 7

62 _____ 89 __ - 27 _ 1

74 _______ 67 __ 7 __4

78 ______ 81 __ - 3 __ 6

88 ______ 92 __ - 4 __5

71 _______ 81 __ - 10 __3

Ranking the data:

27, 13, 10, 7, 4, 3, 2

Observation 5 :

Before = 78 ; After = 81

Difference ; 78 - 81 - 3

Observation 5 = Rank 6

Ranks with negative difference, T = 6 + 5 + 3 + 1 = 12

Ranks with negative difference T+ = (2 + 7 + 4) = 13