The college theater department recently staged a production of a modern musical.
ID: 3221377 • Letter: T
Question
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 315 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. Chi-Square Distribution Degrees of Freedom 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 (to three decimal places X2 critical value (to two decimal places) Conclusion: Reject the null hypothesis; the distribution of gender for theater goers is significantly different from that of the general college O Reject the null hypothesis; the distribution of gender for theater goers is not significantly different from that of the general college O Fail to reject the null hypothesis; the distribution of gender for theater goers is significantly different from that of the general college O Fail to reject the null hypothesis; the distribution of gender for theater goers is not significantly different from that of the general collegeExplanation / Answer
Q.1 N = 215 + 315 = 530
Observed Table
Expected table
X2= (215 - 265)2 /265 + ( 315 - 265)2 /265 = 18.87
for alpha = 0.05 and dF = 2-1= 1; X2critical =3.841
so X2 > X2critical ; reject the null hypothesis; the distribution of gender for theatre goers is significantly different from that of the general college. [ option A]
Q.2
Q.1 N =83 + 97 = 180
Observed Table
Expected table
X2= (90 - 83)2 /90 + ( 90 - 97)2 /90 = 1.09
for alpha = 0.05 and dF = 2-1= 1; X2critical =3.841
so X2 < X2critical ; we fail to reject the null hypothesis; the distribution of gender for men's basketball fans is not significantly different from that of the general college. [ option B]
Male Female Observed 215 315