Question

Flextime, which allows employees to design their own 40-hour work week may be one way to combat problems associated with motivation and absenteeism. One large manufacturing firm was considering implementing flextime for its employees, depending on the success or failure of a pilot program. Ten employees were randomly selected and given a questionnaire designed to measure their attitude toward their job. Each was then permitted to design and follow a flextime workday. After six months, attitudes toward their job were again measured. The resulting attitude scores are display in the table below. The higher the score, the more favorable the employee’s attitude toward his or her work. Use a nonparametric test procedure to evaluate the success of the pilot flextime program. Test using α

Employee	Before	After	Employee	Before	After
1	54	68	6	82	88
2	25	42	7	94	90
3	80	80	8	72	81
4	76	91	9	33	39
5	63	70	10	90	93

Answer 1

Employee Before After Difference After-Before 54 25 80 76 63 82 94 72 68 42 80 91 70 14 17 15 5 6 90 81 39 93 -4 6 10 90

Use Wilcoxon Signed Rank Test: Difference=After-Before

$Let~\theta~be~population~median~of~difference.~Then~\\ Null~hypothesis,~H_0:\theta=0~vs.`H_1:\theta>0$

We arrange absolute value of difference in increasing order:

0, 3 (+), 4(-), 6(+), 6(+), 7(+), 9(+), 14(+),15(+),17(+)

Then rank these absolute values:

Ignore, 1, 2, 3.5,3.5, 5, 6, 7, 8, 9

(Ignore 0 as it is assumed to occur with zero probability and tied ranks are given what would be the usual average value of the ranks if there had been no ties.)

Wilcoxon test statistic=T=sum of the ranks of positive differences=1+3.5+3.5+5+6+7+8+9=43

p-value=0.009 <0.05

Hence we reject null hypothesis and conclude that flextime, which allows employees to design their own 40-hour work week may be one way to combat problems associated with motivation and absenteeism.