You may need to use the appropriate technology to answer thisquestion.

Test the following hypotheses by using the

χ²

goodness of fit test.

H0:	pA = 0.40,pB = 0.40, andpC = 0.20
Ha:	Thepopulation proportions are not pA =0.40, pB = 0.40, andpC = 0.20.

A sample of size 200 yielded 80 in category A, 20 in category B,and 100 in category C. Use α = 0.01 and test to seewhether 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 decimalplaces.)

p-value =

State your conclusion.

Reject H₀. We conclude that the proportionsare equal to 0.40, 0.40, and 0.20.Reject H₀. Weconclude that the proportions differ from 0.40, 0.40, and0.20.     Do not rejectH₀. We cannot conclude that the proportionsdiffer from 0.40, 0.40, and 0.20.Do not rejectH₀. We cannot conclude that the proportions areequal 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 testis one-tailed, enter NONE for the unused tail. Round your answersto three decimal places.)

test statistic ≤test statistic ≥

State your conclusion.

Do not reject H₀. We cannot conclude thatthe proportions are equal to 0.40, 0.40, and 0.20.Do not rejectH₀. We cannot conclude that the proportionsdiffer from 0.40, 0.40, and0.20.     Reject H₀.We conclude that the proportions are equal to 0.40, 0.40, and0.20.Reject H₀. We conclude that theproportions differ from 0.40, 0.40, and 0.20.