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10.32 A 2005 study found that 202 women held board seats out of a total of 1,195 seats in the Fortune 100 companies. A 2003 study found that 779 women held board seats out of a total of 5,727 seats in the Fortune 500 companies. Treating these as random samples (since board seat assignments change often), can we conclude that Fortune 100 companies have a greater proportion of women board members than the Fortune 500?
(a) State the hypotheses.
(b) Calculate the sample proportions.
(c) Find the test statistic and its p-value. What is your conclusion at α = .05?
(d) If statistically significant, can you suggest factors that might explain the increase? (Data are from The 2003 Catalyst Census of Women Board Directors of the Fortune 500, and "Women and Minorities on Fortune 100 Boards," The Alliance for Board Diversity, May 17, 2005).
Complete, neat and step-by-step solutions to the two random sample hypothesis are provided in the attached file.