Question

Given the following contingency table, conduct a test for independence at the 1% 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		38		43
2		32		62

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.

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

• p-value < 0.01

• p-value  0.10
• 0.05  p-value < 0.10

d. What is your conclusion?

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

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

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

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

Answer 1

Solution A] H0: The two variables are independent.; HA: The two variables are dependent.

Solution B]

Test statistic= chi^2=

Test statistic= 0.968+0.834+0.645+0.556=3.003

C] P value= 0.08310

.05< p-value < 0.10

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