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 from the distribution for the general college? Test at the .05 level of significance. The total number of participants is 600. Use this to compute the expected frequencies of females and males. So, the expected frequency for females is 600*0.55=330 and the expected frequency for males is 600*0.45=270. The observed frequencies for females and males are 385 and 215 respectively. Thus chi-square = (385-330)^2/330 + (215-270)^2/270. Use the chi-square table to obtain the tabulated Chi-square value and make your conclusion.

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 from the distribution for the general college? Test at the .05 level of significance. Same as above. The total number of participants 180. Obtain the expected frequencies using this number and the observed frequencies given in the problem for females and males.