Question

1. A group of researchers is studying the prevalence of nepotism in the workplace. Nepotism is the practice of giving family members an advantage to get a job over other applicants.

In order to test if nepotism exists in the hiring process, the researchers just looked at situations where there was a job opening with two applicants: one family member and one non-family member. Based purely on chance, the family member should get the job 50% of the time. If nepotism is present, the family member will get the job more than 50% of the time.

Write out the null hypothesis and the alternative hypothesis.

            H₀:

                  H₁:

                  Is this a test of a population mean or proportion?

Is this a right-tailed, left-tailed, or two-tailed test?

After examining a sample of 125 cases, the researchers found that the family member got the job over the non-family member 71 times.

Calculate the sample proportion p.

Calculate the standard deviation of the sampling distribution.

Calculate the p-value and test statistic for this sample proportion.

Draw a line representing the position of the population proportion and the sample proportion on a normal distribution curve below.

Using a significance level of α=0.05 and keeping in mind if this is a right-tailed, left-tailed, or two-tailed test , draw a line on the normal distribution above representing the critical value(s). Then shade the area outside of the critical value(s) representing the critical region.

Is your sample proportion in the critical region? What does this tell you about your null hypothesis H0? (reject or fail to reject H0)

Interpret this conclusion in terms of the claim that nepotism is prevalent in the workplace. Is there sufficient evidence to support this claim?

Answer 1