Curious AP Statistics students wanted to know if there was a relationship between dress code violations and disciplinary actions: did students who violated the dress code receive more suspensions, detention, and work detail. In a blind survey, so the identities of the subjects were unknown to the AP students, the AP Statistics students randomly selected 185 students and were given the results of their survey from school administration regarding dress code violations and disciplinary actions. The results are below: Dress Code Violations
Disciplinary Action         None Less than 5            More than 5
Work Detail 23 18 17
Detention 22 17 15
Suspension 11 27 35

Dress Code Violations
Disciplinary Action         None Less than 5            More than 5 Total
Work Detail 23 18 17
Detention 22 17 15
Suspension 11 27 35

Required:
a. Write the null and alternative hypotheses for a chi-square test of independence on these data.
b. State and verify the conditions for carrying out the chi-squared test for independence.
c. Determine the test statistic, the degrees of freedom, and the P-value.