Question

The admission office of famous university has a policy of offering equal opportunity to all applicants without regard to religion, race, color, height, weight, marital status, sexual orientation, age or gender. Here are some data on recent admission to the university’s first-year class:

gender	admitted	not admitted
female	370	130
male	660	297

perform an appropriate statistical procedure to demonstrate a gender bias in admission

Answer 1

We shall perform chisquare test of independence

The null and alternative hypothesis

H0: There is no relationship between gender and admission

Ha :There is a strong relationship between gender and admission

Test statistic

where Oi : observed frequency

Ei : expected frequency

Expected frequency calculation

	not admitted	admitted	total
female	370	130	500
male	660	297	957
total	1030	427	1457

E(370) = 500*1030/1457= 353.47

E(130) = 500-353,47=146.53

etc

The contingency table

	not admitted	admitted	total
female	370(353.47)	130(146.53)	500
male	660(676.53)	297(280.47)	957
total	1030	427	1457

The expected frequencies are in the parenthesis

Calculation of Chi square

	Oi	Ei	(Oi-Ei)^2/Ei
	370	353.47	0.7730
	130	146.53	1.8647
	660	676.53	0.4039
	297	280.47	0.9742
total			4.0159

Thus

4.0159

degrees of freedom = (2-1)*(2-1) = 1

Note : degrees of freedom = ( number of rows -1) *( number of columns-1)

Pvalue for 4.0159 with df =1 is given by

P value = 0.0451

Since P value < 0.05

We reject H0

There is sufficient evidence to conclude that there is gender bias in admission.

Note : Excel formula for P value "=CHISQ.DIST.RT(4.0159,1)" or we can use chi square table