For the following question, work through all the hypothesis testing steps and pr

Question

For the following question, work through all the hypothesis testing steps and produce an APA style writeup. Do this non-directionally. Also, demonstrate that you can perform the test both using critical values (old way of doing things) and an exact p-value (new way of doing things).

1)Skylar wants to know if a company’s hiring practices are biased. She knows that in the population, women make up 60% of the applicants to this company. She wants to test whether the hiring practices are fair. She gets a sample of the 75 most recent applications and finds that women made up only 50% of people who received job offers. Is this a significant difference? Run through the correct procedure and produce an APA-style writeup.

Explanation / Answer

Null HYpothesis : H0 : There is no difference between proportion of women applicants and proportion of women who received job offers. p = p0 [ where po = 0.6]

Alternative Hypothesis : Ha : There is significant difference between propotion of womean applicants and women who received job offers. p p0

Standard error of proprtion seo = sqrt [ po (1-p0)/ N] = sqrt [ 0.6 * 0.4/75] = 0.0566

Test Statistic ::

we will use Z - test here

Z = (p - po)/ (seo)

Here p = 0.5

Z = (0.5 - 0.6)/  0.0566 = -1.77

As the test in non- directional in nature so we will find critical value for Z, for alpha = 0.05 which is equal to = -1.96

and P - value = 2* Pr( p <= 0.5; 0.6; 0.0566) by normal distribution =  0.076

which is not under the significane level so we can reject the null hypothesis and can say that there is  no difference between proportion of women applicants and proportion of women who received job offers.

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