Question: The student population at the state college consists of 55% females and 45% 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 385 females and 215 males. Is the gender distribution for theater goers significantly different form 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 83 females and 97 males. Is the gender distribution for basketball fans significantly different form the distribution for the general college? Test at the .05 level of significance.