Question

The Dean of Students at a nearby college wishes to investigate whether women are truly underrepresented amongst majors in the STEM disciplines at the school. The Dean knows that 60% of the student body is female but only 53 of the 115 students majoring in STEM fields are female. While this percentage is smaller than expected, the Dean is unsure whether this difference is greater than would be expected by chance. Compute a chi-square test of goodness-of-fit to answer the Dean’s question. (For the purposes of this problem, assume that gender is binary.)

Answer 1

given

chance of female student =60% this implies p=0.6

chance of male student =40% this implies q=1-p=1-0.6=4

total number of students =n=115

so the expected number of female students =E1=n*p =115*0.6 =69

Expected number of male students=E2=46

while Observed number of female students =O1=53

the observed number of male students =O2=115-53 =62

We have to test

H0: distribution of male and female students in STEM major is according to college male-female student distribution that is 60% female and 40% male

H1: distribution is different

so chi square statistics is given by

here k=2 so

DF=K-1 =2-1=1

Hence

Since P-Value is very less so it's less than any level of significance so we reject the H0

so this difference is greater than would be expected by chance