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# Inference

Wage negotiations between your firm and the union representing your workers are about to collapse. There is considerable disagreement about the mean wage level of workers in Plant A and in Plant B. Wages wee set by the old labor agreement reached three years ago and are based strictly on seniority. Although wages are closely controlled by the labor contract, it may not be possible to assume that the variation in wages is the same at both A and B. Furthermore, it is felt that there is a difference between the mean wage levels due to differing patterns of seniority. Managements head labor negotiator want you to develop confidence intervals to estimate the

a. degree of variability in wages, and
b. difference between the mean wage levels

If a difference exists in the means, wage adjustments must be made to bring the lower wages up to the level of the higher ones. Given the sample data on hourly pay below, what adjustments are called for? This is a very sensitive issue, and the managements head labor negotiator feels you can tolerate only one percent probability of error.

Plant number of employees, average pay per hour Standard deviation

A 25 \$22.53 \$9.60
B 21 \$15.50 \$9.33

#### Solution Preview

a. Degree of variability is measured by variance coefficient:
<br>VC1 = SD1 / µ1 = 9.60 / 22.53 = 0.426
<br>VC2 = SD2 / µ2 = 9.33 / 15.50 = 0.602
<br>Since VC2 > VC1, we can say that Plant 2 has a higher degree of variability.
<br>
<br>b. Test the difference between the two means at 1% significance level
<br>Let Md=µ1- µ2= 22.53-15.50= 7.03
<br>Ho: Md = 0 or there's no difference in ...

#### Solution Summary

Wage negotiations between your firm and the union representing your workers are about to collapse. There is considerable disagreement about the mean wage level of workers in Plant A and in Plant B. Wages wee set by the old labor agreement reached three years ago and are based strictly on seniority. Although wages are closely controlled by the labor contract, it may not be possible to assume that the variation in wages is the same at both A and B. Furthermore, it is felt that there is a difference between the mean wage levels due to differing patterns of seniority. Managements head labor negotiator want you to develop confidence intervals to estimate the

a. degree of variability in wages, and
b. difference between the mean wage levels

If a difference exists in the means, wage adjustments must be made to bring the lower wages up to the level of the higher ones. Given the sample data on hourly pay below, what adjustments are called for? This is a very sensitive issue, and the managements head labor negotiator feels you can tolerate only one percent probability of error.

Plant number of employees, average pay per hour Standard deviation

A 25 \$22.53 \$9.60
B 21 \$15.50 \$9.33

\$2.19