Question

The following table contains observed frequencies for a sample of 240.

Row Variable	Column Variable
	A	B	C
P	15	25	15
Q	30	60	25
R	15	20	35

Test for independence of the row and column variables using

α = 0.05.

State the null and alternative hypotheses.

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

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 the column and row variables are not independent.Reject H₀. We conclude that the column variable is not independent of 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.

Answer 1

The statistical software output for this problem is :

.H₀: Variable P is independent of variables Q and R.
H_a: Variable P is not independent of variables Q and R.

Test statistics = 17.595

P-value = 0.0015

Reject H₀. We conclude that the column variable is not independent of the row variable.