Question

In: Statistics and Probability

A company institutes an exercise break for its workers to see the effect on job satisfaction,...

A company institutes an exercise break for its workers to see the effect on job satisfaction, as measured by a questionnaire that assesses workers’ satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the following table. Determine if there is a significant increase in worker job satisfaction after the implementation of the exercise program using a 5% level of significance.

Job Satisfaction Index Table

WORKER NUMBER BEFORE AFTER
1 34 33
2 28 36
3 29 50
4 45 41
5 26 37
6 27 41
7 24 39
8 15 21
9 15 20
10 27 37

Must complete all parts of this problem:

  • PART 1: Use Excel to perform a Matched Pairs Test on the data (di = before – after). Copy and paste the output from Excel into a word document.
  • PART 2: Write 3 - 4 sentences on the findings from the Matched Pairs Test. Is there a significant increase in worker job satisfaction after the implementation of the exercise program using a 5% level of significance? Support your answer by using the output from the test. You must include: the hypotheses for the test, a discussion of the p-value, and the decision you reach and why.

Solutions

Expert Solution

ANSWER:

Part 1: Excel output

Before(X) After(y) di di2
34 33 1 1
28 36 -8 64
29 50 -21 441
45 41 4 16
26 37 -11 121
27 41 -14 196
24 39 -15 225
15 21 -6 36
15 20 -5 25
27 37 -10 100
Total -85 1225
Mean -8.5
Var 50.25
SD 7.088723
tcal -3.79185
tcrit 1.833113
pvalue 0.002141

Formulae

Before(X) After(y) di di2
34 33 =A2-B2 =C2^2
28 36 =A3-B3 =C3^2
29 50 =A4-B4 =C4^2
45 41 =A5-B5 =C5^2
26 37 =A6-B6 =C6^2
27 41 =A7-B7 =C7^2
24 39 =A8-B8 =C8^2
15 21 =A9-B9 =C9^2
15 20 =A10-B10 =C10^2
27 37 =A11-B11 =C11^2
Total =SUM(C2:C11) =SUM(D2:D11)
Mean =C12/10
Var =(D12/10)-(C13^2)
SD =SQRT(C14)
tcal =C13/(C15/SQRT(10))
tcrit =TINV(2*0.05,9)
pvalue =TDIST(3.79,9,1)

Part 2:

There is no significant increase in worker job satisfaction after the implementation of exercise of the program

Vs

: There is significant increase in worker job satisfaction after the implementation of exercise of the program

Under , the test statistic is

            

Here, and

Since , we may reject

We may conclude that, there is significant increase in worker job satisfaction after the implementation of exercise of the program.

-value=0.002141

Also, p-value <0.05 (level of significance), we may reject .

We may conclude that, there is significant increase in worker job satisfaction after the implementation of exercise of the program.

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