est the following hypotheses by using the x² goodness of fit test. Hoi PA = 0.40, Pg = 0.40, and pe = 0.20 H: The population proportions are not paA = 0.40, Pg = 0.40, and Pc = 0.20. sample of size 200 yielded 20 in category A, 60 in category B, and 120 in category C. Use a = 0.01 and test to see whether the proportions are as stated in Ho: a) Use the p-value approach. Find the value of the test statistic. 35 ]× Find the p-value. (Round your answer to four decimal places.) p-value = State your senclusion.

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Test the following hypotheses by using the x? goodness of fit test.
Ho: PA = 0.40, PR = 0.40, and p. = 0.20
H: The population proportions are not pa = 0.40, PR = 0.40, and P. = 0.20.
A sample of size 200 yielded 20 in category A, 60 in category B, and 120 in category C. Use a = 0.01 and test to see whether the proportions are as stated in Ho:
(a) Use the p-value approach.
Find the value of the test statistic.
35
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
O Do not reject H,. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.
O Reject H,. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.
O Reject H. We conclude that the proportions differ from 0.40, 0.40, and 0.20.
O Do not reject H. We cannot 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 s
test statistic 2
State your conclusion.
O Reject H,. We conclude that the proportions differ from 0.40, 0.40, and 0.20.
O Do not reject H.. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.
O Do not reject H.. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.
O Reject Ho. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.
Transcribed Image Text:You may need to use the appropriate technology to answer this question. Test the following hypotheses by using the x? goodness of fit test. Ho: PA = 0.40, PR = 0.40, and p. = 0.20 H: The population proportions are not pa = 0.40, PR = 0.40, and P. = 0.20. A sample of size 200 yielded 20 in category A, 60 in category B, and 120 in category C. Use a = 0.01 and test to see whether the proportions are as stated in Ho: (a) Use the p-value approach. Find the value of the test statistic. 35 Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not reject H,. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. O Reject H,. We conclude that the proportions are equal to 0.40, 0.40, and 0.20. O Reject H. We conclude that the proportions differ from 0.40, 0.40, and 0.20. O Do not reject H. We cannot 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 s test statistic 2 State your conclusion. O Reject H,. We conclude that the proportions differ from 0.40, 0.40, and 0.20. O Do not reject H.. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. O Do not reject H.. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. O Reject Ho. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.
Expert Solution
Working
Observed Expected (O-E)^2 (O-E)^2/E
20 80 3600 45
60 80 400 5
120 40 6400 160
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