Question

Given the following contingency table, conduct a test for independence at the 10% significance level. (You may find it useful to reference the appropriate table: chi-square table or F table)

	Variable A
Variable B		1		2
1		39		34
2		34		74

a. Choose the null and alternative hypotheses.

• H₀: The two variables are independent.; H_A: The two variables are dependent.

• H₀: The two variables are dependent.; H_A: The two variables are independent.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

d. What is your conclusion?

• Do not reject H₀; we cannot conclude that the two categories are dependent.

• Reject H₀; we cannot conclude that the two categories are dependent.

• Do not reject H₀; we can conclude that the two categories are dependent.

• Reject H₀; we can conclude that the two categories are dependent

Answer 1

The statistical software output for this problem is :

(a)

H₀: The two variables are independent.; H_A: The two variables are dependent.

(b)

Test statistics = 8.715

(c)

P-value < 0.01

(d)

Reject H₀; we can conclude that the two categories are dependent