Question

The following table contains observed frequencies for a sample of 200.

Column Variable

Row Variable A B C

P 30 56 65

Q 20 14 15

If you cant read it AP=30 AQ=20 BP=56 BQ=14 CP=65 CQ=15

Test for independence of the row and column variables using a =.05. Compute the value of the x^2 test statistic (to 2 decimals). The p-value=?

Answer 1

here applying chi square test:

Observed	Oi	A	B	C	Total
	P	30	56	65	151
	Q	20	14	15	49
	total	50	70	80	200
Expected	Ei=row total*column total/grand total	A	B	C	Total
	P	37.75	52.85	60.40	151
	Q	12.25	17.15	19.60	49
	total	50	70	80	200
chi square    χ2	=(Oi-Ei)2/Ei	A	B	C	Total
	P	1.5911	0.1877	0.3503	2.129
	Q	4.9031	0.5786	1.0796	6.561
	total	6.494	0.766	1.430	8.690

test statistic X² =8.69

p value =0.0130