Question

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

Row Variable	Column Variable
	A	B	C
P	24	48	54
Q	26	22	26

Test for independence of the row and column variables using

α = 0.05.

State the null and alternative hypotheses.

H₀: The column variable is independent of the row variable.
H_a: The column variable is not independent of the row variable.H₀: Variable P is not independent of variable Q.
H_a: Variable P is independent of variable Q.    H₀: The column variable is not independent of the row variable.
H_a: The column variable is independent of the row variable.H₀: Variable P is independent of variable Q.
H_a: Variable P is not independent of variable Q.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that there is an association between the column variable and the row variable.Do not reject H₀. We cannot conclude that the column and row variables are independent.    Reject H₀. We conclude that the column and row variables are independent.Reject H₀. We conclude that there is an association between the column variable and the row variable.

Answer 1

H₀: The column variable is independent of the row variable.
H_a: The column variable is not independent of the row variable

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	A	B	C	Total
	P	31.5000	44.1000	50.4000	126
	Q	18.5000	25.9000	29.6000	74
	total	50	70	80	200
chi square    χ2	=(Oi-Ei)2/Ei	A	B	C	Total
	P	1.786	0.345	0.257	2.3878
	Q	3.041	0.587	0.438	4.0656
	total	4.8263	0.9322	0.6950	6.4534
test statistic X2 =		6.453

p value =

0.0397

Reject H₀. We conclude that the column and row variables are independent.