Question

Is a person's favorite pizza topping dependent on their gender? A random sample of pizzas ordered and the gender of the person who ordered were recorded and the results are found in the table below. Use this data to test whether or not pizza topping preference is independent of gender at the  α=0.10α=0.10 level of significance.  

Which would be correct hypotheses for this test?

H0:H0:Pizza topping preference and gender are independent;  H1:H1:There is some relationship between a person's gender and their pizza topping preference

H0:p1=p2H0:p1=p2;  H1:p1≠p2H1:p1≠p2

H0:H0: Pizza topping preference is dependent on gender;  H1:H1: Pizza topping preference and gender are independent

H0:μ1=μ2H0:μ1=μ2;  H1:μ1≠μ2H1:μ1≠μ2

Sample data:

	Cheese	Pepperoni	Sausage	Mushroom	Veggie
Female	11	22	5	5	18
Male	10	20	20	20	4

Test Statistic:



Give the P-value:



Which is the correct result:

Reject the Null Hypothesis

Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

There is sufficient evidence to suggest that there is a relationship between pizza topping preference and gender

There is not enough evidence of any relationship between pizza topping preference and gender

Answer 1

Observed
	Cheese	Pepporoni	Sausage	Mushroom	Veggie	total
Female	11	22	5	5	18	61
Male	10	20	20	20	4	74
Total	21	42	25	25	22	135

Expected frequencies are calculated as

Ei = sum(coli)*sum(rowi)/total

Expected
	Cheese	Pepporoni	Sausage	Mushroom	Veggie
Female	9.489	18.978	11.296	11.296	9.941
Male	11.511	23.022	13.704	13.704	12.059

Test statistic, chi-square = sum((Oi - Ei)^2/Ei) =  26.04

H0:Pizza topping preference and gender are independent
H1:There is some relationship between a person's gender and their pizza topping preference

Test Statistic: 26.04

Give the P-value: 0.000031

Which is the correct result:

Reject the Null Hypothesis: Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?
There is sufficient evidence to suggest that there is a relationship between pizza topping preference and gender