Question: As treasurer, Ray sees all NYSMATYC incoming membership applications. At a recent board meeting, Christine expressed concern that the proportion of CUNY math teachers being members of NYSMATYC is lower than for SUNY. To test the claim, Ray determined that 45 of 130 full time math faculty from CUNY are members of NYSMATYC, and that 120 of 274 full time math faculty from SUNY are members of NYSMATYC. Construct a 95% confidence interval for the difference in the two proportions. Can we say that SUNY math faculty are more likely to be members of NYSMATYC than CUNY math faculty?