Question

The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α=0.1 level of significance.

	Category 1	Category 2	Category 3
Failures	70	76	52
Successes	58	52	71

State the hypotheses. Choose the correct answer below.

A. H0​: The categories of the variable and success and failure are dependent.

H1​: The categories of the variable and success and failure are independent.

B. H0​: The categories of the variable and success and failure are independent.

H1​: The categories of the variable and success and failure are dependent.

C. H0​: μ1=E1 and μ2=E2 and μ3=E3

H1​: At least one mean is different from what is expected.

D. H0​: p1=p2=p3

H1​: At least one of the proportions is different from the others.

What is the​ P-value?

____ (Round to three decimal places as​ needed.)

What conclusion can be​ made?

A.The​ P-value is greater than or equal to α​, so do not reject H0. There is sufficient evidence that the categories of the variable and success and failure are dependent.

B.The​ P-value is less than α​, so reject H0. There is sufficient evidence that the proportions are different from each other.

C.The​ P-value is greater than or equal to α​, so reject H0. There is not sufficient evidence that the proportions are different from each other.

D.The​ P-value is less than α​, so do not reject H0. There is not sufficient evidence that the categories of the variable and success and failure are dependent.

Answer 1