Question

A random sample of females from a certain population yields
the following counts on their preferences for different pizzas:
Cheese: 15, Sausage: 59, and Pepperoni: 26,
An independent random sample of males from the same population yields
the following counts on their preferences for different pizzas:
Cheese: 15, Sausage: 26, and Pepperoni: 59,
You are to test the null hypothesis that there is no difference in pizza prefrences of females as compared to males.
Calculate the p-value of the chi-square of test of homogeneity.

Answer 1

Applying chi square test of homogeneity

Observed		Cheese	Sausage	Pepperoni	Total
	Female	15	59	26	100
	Male	15	26	59	100
	total	30	85	85	200
Expected	Ei=row total*column total/grand total	Cheese	Sausage	Pepperoni	Total
	Female	15.000	42.500	42.500	100.00
	Male	15.000	42.500	42.500	100.00
	total	30.00	85.00	85.00	200.00
chi square    χ2	=(Oi-Ei)2/Ei	Cheese	Sausage	Pepperoni	Total
	Female	0.000	6.406	6.406	12.8118
	Male	0.000	6.406	6.406	12.8118
	total	0.0000	12.8118	12.8118	25.624
test statistic X2 =		25.6235
p value =		0.0000

since p value is significantly low we reject null hypothesis