In this test, I would use a one-tailed test. The objective of this test is to determine whether the company's hiring process had instances of discrimination or not. In this case, 20% of the hired individuals were minorities while making up 28% of the total candidates. In this case, the test is done to determine if the percentage of hired minorities is greater than the expected number; they could be many or few. The plaintiff is unlikely to sue the company for discrimination if the number of minorities hired exceeded the expected number. This test's hypothesis is: the number of minorities hired is greater or equal to the expected proportion. This test requires a one-tailed test. According to UCLA (2016), this test is used to determine the relationship of variables in one direction. In this case, the test investigates the relationship between hiring and discrimination in one direction. The test investigates if the number of hired minorities exceeded or was equal to the expected proportion.
In this test, the Type I error would be concluding that the number of hired minorities is less than the expected number and that the organization's hiring practices were discriminatory while it was not the case. According to McLeod (2019), a type I error happens when a null hypothesis is incorrectly rejected, resulting in a false positive. Therefore, rejecting the null hypothesis incorrectly and concluding that the company discriminated against the minorities would be a type I error. On the other hand, the Type II error will be concluding that the company hired many minorities hence not discriminating while the company hired few minorities and is discriminating.
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In case the hypothesis is tested at a 5% significance instead of 10%, the power of the test will be reduced. Additionally, if the plaintiff used a sample of 40 hires, the likelihood of committing a type II error would be reduced. Typically, the likelihood of type II error is obtained by subtracting one from the test's power. The test's power can be increased by increasing the size of the sample. In this case, the sample size is increased from 20 to 40; therefore, the risk of committing type II error will be reduced.
Based on my analysis, the next step should be testing the hypothesis to determine whether the company is discriminatory. Conducting this test would require that the sample size be increased to increase the test's accuracy and reduce the chances of a Type II error.
References
McLeod, S. (2019, July 04). What are Type I and Type II Errors? Simply Psychology . https://www.simplypsychology.org/type_I_and_type_II_errors.html#:~:text=A%20type%201%20error%20is,rejects%20a%20true%20null%20hypothesis.&text=The%20probability%20of%20making%20a,you%20reject%20the%20null%20hypothesis.
UCLA. (2016, February). What are the Differences between One-Tailed and Two-Tailed Tests? UCLA: Institute for Digital Research & Education . https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-the-differences-between-one-tailed-and-two-tailed-tests/
