The article “Student-Faculty Interaction in Research Universities” (Res. High. Educ. 2009: 437–459) reported that 20.4% of 3168 students from lower-class families said they frequently talked with faculty outside class about course material. The corresponding percentages for the 16,774 middle-class students and 8188 upper-class students were 18.6% and 20.2%, respectively. Does this data suggest that social class of a student is independent of whether or not he/she frequently talked with faculty outside class about course material?

a. Carry out an appropriate test of hypotheses.
b. In light of the sample sizes used in this study, why is the result in (a) not surprising?