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Recent studies have investigated the relationship between gender and career advancement. The following data represent a random sample of mathematicians classified by gender and academic rank: Test if there is a relationship between gender and academic rank using a 5% level of significance. Academic Rank gender Instructor Assistant Associate Full Total Professor Professor Professor Female 12 15 18 7 52 Male 21 25 30 22 98 Total 33 40 48 29 150 1. State the null and alternative hypothesis. Ho: gender and academic rank are not independent Hi: gender and academic rank are independent b. Ho: gender and academic rank are the same Hi: gender and academic rank are not the same C. Ho: gender and academic rank are independent Hi: gender and academic rank are not independent d. Ho: gender and academic rank have the same mean Hj: gender and academic rank do not have the same rank 2. What is the critical value of the test and your decision rule? a. 7.82; Reject Ho if the test statistic is greater than or equal to 7.82, otherwise not enough evidence to reject Ho. b. 1.77; Reject Ho if the test statistic is greater than or equal to 1.77, otherwise not enough evidence to reject Ho. C. 1.645; Reject Ho if the test statistic is greater than or equal to 1.645, otherwise not enough evidence to reject Ho. d. 7.38; Reject Ho if the test statistic is greater than or equal to 7.38, otherwise not enough evidence to reject Ho. 3. What is the test statistic? a. 7.82 b. 1.77 c. 1.645 d. 7.38 4. State your conclusion. a. Reject Ho: b. Not enough evidence to reject Ho