A large company is being sued for gender discrimination because 20% of newly hir

Question

A large company is being sued for gender discrimination because 20% of newly hired candidates are women when 40% of all applicants were women. You plan to use hypothesis testing to determine whether there is significant evidence that the company's hiring practices are discriminatory.

Part A: State the null and alternative hypotheses for the significance test. (2 points)

Part B: In the context of the problem, what would a Type I error be? A Type II error? (2 points)

Part C: If the hypothesis is tested at a 1% level of significance instead of 5%, how will this affect the power of the test? (3 points)

Part D: If the hypothesis is tested based on the hiring of 1,000 employees rather than 100 employees, how will this affect the power of the test

Explanation / Answer

Null Hypothesis : H0: The hiring practices of Company is not discriminatry. The proportion of women hired candiates is same as proportion of applicants. p = 0.40

Alternative Hypothesis : Ha : The hiring practices of Company is discriminatry. The proportion of women hired candiates is significantly less than the proportion of applicants. p < 0.40

Part B

here type I error is when we reject the null hypothesis even if it is true so in this case we will accept that company's policy is discriminatory to women applicants even if it is not true,,

Here type II error is when we failed to reject the null hypothesis even if it is false so in this case we will accept that the company's policy is not discriminatory to women even if policy of company are anti - women.

Part(C)

Here if the hypothesis is tested at 1% level os significance instead of 5%, that mean the rejection region will increase so that will decrease the power of the test.

Part (D)

If hiring sample size is increased to 1000 employees rather than 100 employee that will reduce the standard error of proportion and ultimately reduce the range of rejection so that wil increase the power of the test.

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