Question

Consider the following contingency table of observed frequencies. Complete parts a. through d. below.

Click the icon to view the contingency table.

Column Variable

Row Variable    C1 C2    C3

R1 11    9 12

R2 11    6 6

a. Identify the null and alternative hypotheses for a​ chi-square test of independence with based on the information in the table. This test will have a significance level of alpha α=0.01. Choose the correct answer below.

A. H0​: The row and column variables are not independent of one another. H1​: The row and column variables are independent of one another.

B. H0​: The variables R1​, R2​, C1​, C2​, and UpperC3 are independent. H1​: At least one of the variables is not independent.

C. H0​: The variables R1​, R2​, C1​, C2​, and C3 are independent. H1​: None of the variables are independent.

D. H0​: The row and column variables are independent of one another. H1​: The row and column variables are not independent of one another. ​

b, Calculate the expected frequencies for each cell in the contingency table.

Column Variable

Row Variable    C1 C2    C3

R1

R2

​(Round to two decimal places as​ needed.)

c. Calculate the​ chi-square test statistic.

χ2=(Round to two decimal places as​ needed.)

d. Determine the​ p-value. Using alpha α=0.01​, state your conclusions. ​

p-value= ​(Round to three decimal places as​ needed.) State your conclusions.

The​ p-value is (greater than/less than) alpha α= 0.01​, so (reject/do not reject) H0. There is (sufficient/insufficient) evidence to indicate that (the row and column variables are not independent of one another//at least one of the variables is not independent//the row and column variables are independent of one another. /none of the variables are independent/ the variables R1, R1, C1, C2, and C3 are independent. (pick one) Click to select your answer(s).

Answer 1