Question

ach individual in a random sample of high school and college students was cross-classified with respect to both political views and marijuana usage, resulting in the data displayed in the accompanying two-way table. Does the data support the hypothesis that political views and marijuana usage level are independent within the population? Test the appropriate hypotheses using level of significance 0.01.

		Usage Level
		Never	Rarely	Frequently
Political Views	Liberal	478	171	116
	Conservative	211	49	13
	Other	174	47	86

State the appropriate hypotheses.

H₀: p_ij =

p_i·

p_·j

    i = 1, 2, 3; j = 1, 2, 3
H_a: at least one p_ij ≠

p_i·

p_·j

H₀: p_ij = p_i· · p_·j    i = 1, 2, 3; j = 1, 2, 3

H_a: at least one p_ij ≠

p_i· · p_·j

    H₀: p_ij ≠

p_i·

p_·j

    i = 1, 2, 3; j = 1, 2, 3
H_a: at least one p_ij =

p_i·

p_·j

H₀: p_ij ≠ p_i· · p_·j    i = 1, 2, 3; j = 1, 2, 3

H_a: at least one p_ij =

p_i· · p_·j

Calculate the test statistic. (Round your answer to two decimal places.)
χ² =

What can be said about the P-value for the test?

P-value < 0.0050.005 < P-value < 0.01    0.01 < P-value < 0.0250.025 < P-value < 0.050.05 < P-value < 0.10P-value > 0.10

State the conclusion in the problem context.

Reject H₀. There is no evidence that political views and level of marijuana usage are related.Fail to reject H₀. There is no evidence that political views and level of marijuana usage are related.    Reject H₀. There is evidence that political views and level of marijuana usage are related.Fail to reject H₀. There is evidence that political views and level of marijuana usage are related.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

The statistical software output for this problem is :

B

Test statistics = 66.06

P-value < 0.005

Reject H₀. There is evidence that political views and level of marijuana usage are related.