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 40 in category A, 20 in category B, and 140 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:

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

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

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

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

(b) 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:

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

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

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

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