In: Statistics and Probability
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:
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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