Test the following hypotheses by using the ² goodness of fit test.

H0:	pA = 0.40, pB = 0.40, and pC = 0.20
Ha:	The population proportions are not pA = 0.40, pB = 0.40, and pC = 0.20.

A sample of size 200 yielded 20 in category A, 60 in category B, and 120 in category C. Use = 0.01 and test to see whether the proportions are as stated in H₀.

(a)Use the p-value approach.

Find the value of the test statistic.

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

a. Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.

b. Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.

c. Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.

d. Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.

Repeat the test using the critical value approach.

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.)

test statistic

test statistic

State your conclusion.

a. Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.

b. Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.

c. Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.

d. Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.