The student population at the state college consists of 60% females and 40% males.

a. The college theater department recently staged a production of a modern musical. A researcher recorded the gender of each student entering the theater and found a total of 37 females and 18 males. Is the gender distribution for theater goers significantly different from the distribution for the general college? Test at the .05 level of significance.

b. The same researcher also recorded the gender of each student watching a men’s basketball game in the college gym and found a total of 58 females and 82 males. Is the gender distribution for basketball fans significantly different from the distribution for the general college? Test at the .05 level of significance.