Question

A random sample of 400 men and 400 women was randomly selected and asked whether they planned to attend a concert in the next month. The results are listed below. Perform a homogeneity of proportions test to test the claim that the proportion of men who plan to attend a concert in the next month is the same as the proportion of women who plan to attend a concert in the next month. Use α = 0.04.

	men	women
plan to attend concert	230	255
do not plan to attend	170	145

Answer 1

null hypothesis: Ho:  the proportion of men who plan to attend a concert in the next month is the same as the proportion of women who plan to attend a concert in the next month

Alternate hypothesis: Ha : the proportion of men who plan to attend a concert in the next month is not the same as the proportion of women who plan to attend a concert in the next month

degree of freedom(df) =(rows-1)*(columns-1)=		1
for 1 df and 0.04 level , critical value       χ2=		4.218
Decision rule : reject Ho if value of test statistic X2>4.218

Applying chi square test of homogeneity

Expected	Ei=row total*column total/grand total	men	women	Total
	plan to attend	242.50	242.50	485
	do not plan to attend	157.50	157.50	315
	total	400	400	800
chi square    χ2	=(Oi-Ei)2/Ei	men	women	Total
	plan to attend	0.644	0.644	1.2887
	do not plan to attend	0.992	0.992	1.9841
	total	1.6364	1.6364	3.2728
test statistic X2 =		3.273

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that proportions are different.