1. A company is evaluating the impact of a wellness program offered on-site as a
ID: 3128165 • Letter: 1
Question
1.A company is evaluating the impact of a wellness program offered on-site as a means of reducing employee sick days. A total of 8 employees agree to participate in the evaluation which lasts 12 weeks. Their sick days in the 12 months prior to the start of the wellness program and again over the 12 months after the completion of the program are recorded and are shown below. Is there a significant reduction in the number of sick days taken after completing the wellness program? Use the Sign Test at a 5% level of significance.
Complete the table below.
Employee
Sick Days Taken in 12 Months Prior to Program
Sick Days Taken in 12 Months Following program
Difference (Reduction = Prior-After )
Sign
1
8
7
( 1 )
( + )
2
6
6
( 0 )
( + )
3
4
5
( -1)
( - )
4
12
11
( 1 )
( + )
5
10
7
( 3 )
( + )
6
8
4
( 4)
( + )
7
6
3
( 3 )
( + )
8
2
1
( 1 )
(+ )
Alpha= __0.05______
n= _____8___
Critical value= ________
Smaller of the number of positive or negative signs= ________
Based on comparing the smaller of the number of positive or negative signs to the Critical value which of the following is (are) true?
There is statistically significant evidence at alpha=0.05 to show that the median difference (reduction) is positive.
There is not statistically significant evidence at alpha=0.05 to show that the median difference (reduction) is positive.
There are not enough data points to reach a conclusion.
The tied value makes the analysis suspect.
Employee
Sick Days Taken in 12 Months Prior to Program
Sick Days Taken in 12 Months Following program
Difference (Reduction = Prior-After )
Sign
1
8
7
( 1 )
( + )
2
6
6
( 0 )
( + )
3
4
5
( -1)
( - )
4
12
11
( 1 )
( + )
5
10
7
( 3 )
( + )
6
8
4
( 4)
( + )
7
6
3
( 3 )
( + )
8
2
1
( 1 )
(+ )
Explanation / Answer
Critical value 1
Smaller of number of negative signs = 1
Since test statistic is < = critical value we reject Ho and conclude that there is enough evidence that there is significant reduction
Answer is
There is statistically significant evidence at alpha=0.05 to show that the median difference (reduction) is positive.
Critical value 1
Smaller of number of negative signs = 1
Since test statistic is < = critical value we reject Ho and conclude that there is enough evidence that there is significant reduction
Answer is
There is statistically significant evidence at alpha=0.05 to show that the median difference (reduction) is positive.
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