Question

A government study of hiring practices is to be done. It is felt that the proportion of minorities hired by heavy industry should reflect the proportion of minorities living in the area which is 20%. Too high a proportion may indicate favoritism in hiring, while too low a proportion may indicate discrimination. A random sample of 130 recent hires in heavy industry finds 14 were minority applicants.

a. Is there evidence of significant hiring irregularities? Test using = .01. (20)

b. What type of error might you have made with your test in part A? Explain carefully in this context. (5)

Answer 1

(a) We use the Hypothesis test for proportion. = 14 / 130 = 0.108

(a) The Hypothesis:

H0: p = 0.2

Ha: p    0.2

This is a 2 Tailed Test.

The Test Statistic:

The p Value:    The p value (2 Tail) for Z = -2.62, is; p value = 0.0088

The Critical Value:   The critical value (2 tail) at = 0.01, Zcritical = +2.576 and -2.576

The Decision Rule:    

The Critical Value Method: If Zobserved is > Zcritical or if Zobserved is < -Zcritical, Then Reject H0.

The p value Method: If the P value is < , Then Reject H0

The Decision:   

The Critical Value Method: Since Z observed (-2.62) is < -Zcritical (-2.576), We Reject H0.

The p value Method: Since P value (0.0088) is < (0.01), We Reject H0.

The Conclusion: There is sufficient-insufficient evidence at the 99% significance level to conclude that the proportion in hiring is different from 0.2. There are hiring irregularities.

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(b) Since we have rejected the Null Hypothesis in (a), it is possible that it could have been true and we have made an error in rejecting a true null hypothesis.

This error, is called a Type I error.

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