Jail inmates can be classified into one of the following four categories according to the type of crime committed: violent crime, crime against property, drug offenses, and public-order offenses. Suppose that random samples of 500 male inmates and 500 female inmates are selected, and each inmate is classified according to type of offense. The data in the accompanying table are based on summary values given in the article

“Profile of Jail Inmates” (USA Today, April 25, 1991). We would like to know whether male and female inmates differ with respect to type of offense.
Gender Type of Crime Male Female Violent 117 66 Property 150 160 Drug 109 168 Public-Order 124 106

a. Is this a test of homogeneity or a test of independence?

b. Test the relevant hypotheses using a significance level of .05.