Question

A health tech company is interested in investigating whether there is a gender bias in the workplace. Specifically, they collect information about how many female and male employees work at the company in following positions: entry-level, mid-level management (referred as mid-level) and high-level management (referred as high-level). They are asking for your help to find out if gender and job position are independent from each other or if there is a relationship between these factors indicating a gender bias. Table 4 shows the counts in each factor level combination.

Part a. Which statistical test would you recommend for this study? Explain your response. (Short answer, 1 point)

Part b. Observed values (O_ij for i=1,2 for gender and j=1,2,3 for position) are given in Table 4. Compute the Expected values matrix and report all E_ij values in the expected values matrix. (Essay style, 3 points)

Part c. Compute the appropriate test statistic. What is its value? Compare it to the critical value from the corresponding Table in Appendix B in Rice. What is the statistical decision at the significance level 0.05? Is there a gender bias at this company? (Essay style, 3 points)

	Position
Gender	entry-level	mid-level	high-level
Female	38	14	6
Male	20	16	15

Answer 1