Question

There appears to be a gender difference in elections for the U.S. Presidency. Women are typically more likely to vote for the Democratic candidate than men. A small sample of people working at a factory has been asked about their political party preference and their responses are recorded below. Do their responses indicate a significant relationship between gender and party preference?

Party Preference Gender Male Female Total Democrat 10 15 25 Republican 15 10 25 Total 25 25 50

Answer 1

null hypothesis: Ho: gender and party preference are independent

Alternate hypothesis:Ha: gender and party preference are dependent

degree of freedom(df) =(rows-1)*(columns-1)=

1

for 1 df and 0.05 level of signifcance critical region       χ2=

3.841

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Male	Female	Total
	Democrat	12.500	12.50	25
	Republican	12.50	12.50	25
	total	25	25	50
chi square    χ2	=(Oi-Ei)2/Ei	Male	Female	Total
	Democrat	0.5000	0.5000	1.000
	Republican	0.5000	0.5000	1.000
	total	1.000	1.000	2.000

Test statistic X² =2.000

as test statisitcs is not greater then critical value we can not reject null hypothesis

we do not have evidence to conclude that there is a significant relationship between gender and party preference