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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