Question

(Please answer sub parts: A, B)

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 significance level using CV = 3.84).

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 significance level
using CV = 3.84).

Answer 1

let

P1 is proportion of ffemales and P2 is proportion of males

a)

Here we have to test that  college theater department have different proportion of male and females students

Hence

H0: P1=0.55 P2=0.45

Ha: proportions are different from given proportion

we have observed Values O1=385 O2=215

Here N=385+215=600

so expected frequencies are given by

E1=N*P1=600*0.55=330

E2=N*P2=600*0.45=270

so test statistics is given by

since CHi square statistics is greater than critical value hence gender distribution for theater goers significantly different from the distribution for the general college

b)

Here observed Values are

O1=83 O2=97

N=83+97=180

now expected frequencies are given by

E1=N*P1=180*0.55=99

E2=N*P2=180*0.45 =81

now test statistics is given by

since chi square statistics is greater than ciritcal value hence we reject H0 hence

the gender distribution for basketball fans significantly different from the distribution for the general college