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Hypothesis Test on Proportions

The company you work for employs 585 assembly-line workers - 526 men and 59 women. 16 men and 10 women have been laid off.

Of the 526 male assembly-line workers, 134 were over 40 years of age. 12 of the 16 laid off men are over 40 years of age. Those 12 men are alleging that they were discriminated against because of their age.

a) Construct the strongest possible argument that the 12 laid off men over 40 years of age could make in favor of their assertion that they have been discriminated against.

b) The 134 male workers over 40 years of age earned a mean of $38,762, while the 392 male workers under the age of 40 earned a mean of $36,894. Does this information strengthen or weaken the argument made in a)? Give reasons for your answer.

c) The company argues that the men could always have found a cut-off age above and below which the proportions of workers laid off would be different from one another. If it hadn't been 40, it might have been 35 or 30, or 45 or 50; but there would always be some age that would divide the workers into two groups that would appear to have been treated differently. Is this argument valid? Explain your answer.

Solution Preview

The company you work for employs 585 assembly-line workers - 526 men and 59 women. 16 men and 10 women have been laid off.

Of the 526 male assembly-line workers, 134 were over 40 years of age. 12 of the 16 laid off men are over 40 years of age. Those 12 men are alleging that they were discriminated against because of their age.

a) Construct the strongest possible argument that the 12 laid off men over 40 years of age could make in favor of their assertion that they have been discriminated against.

They can argue that they were discriminated against if they were disproportionately laid off from the company. Of the male assembly line workers, 25.5% are over 40 (134/526 = 0.25475), and of the men who were laid off, 75% are over 40 (12/16 = 0.75). It seems like there was bias against the older men because 75% is so much larger than 25.5%, but we have to do a statistical test to make sure.

We're comparing proportions, so we have to use a z-test. It is a two-proportion z-test because we're comparing two proportions instead of one proportion to ...

Solution Summary

The solution to the 3-part question uses a z-test to determine if there is evidence of discrimination against older workers.

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