1. A recent study investigated if the distribution of gender is the same across all academic ranks. Data were collected by taking a random sample of individuals from within each academic rank and then recording each individuals gender. Use the output below to conduct the appropriate hypothesis test. Use a 0.05 level of significance.

a) Null and alternative hypotheses

b) Test Statistic value

c) p-value

The SAS System The FREQ Procedure Frequency Table of gender by career Percent gender career Row Pct Instructor Assistant Prof Associate Prof Full Prof Total Col Pct Female 12 15 18 7 52 8.00 10.00 12.00 4.67 34.67 23.08 28.85 34.62 13.46 36.36 37.50 37.50 24.14 Male 21 25 30 22 98 14.00 16.67 20.00 14.67 65.33 21.43 25.51 30.61 22.45 63.64 62.50 62.50 75.86 Total 33 40 48 29 150 22.00 26.67 32.00 19.33 100.00 Statistics for Table of gender by career Statistic DF Value Prob Chi-Square 3 1.7733 0.6208 Likelihood Ratio Chi-Square 3 1.8561 0.6028 Mantel-Haenszel Chi-Square 1 0.7649 0.3818 Phi Coefficient 0.1087 Contingency Coefficient 0.1081 Cramer's V 0.1087