Test the following hypotheses by using the χ ^{2} goodness of fit test.
H _{0}: | p _{A} = 0.2, p _{B} = 0.4, and p _{C} = 0.4 |
H_{a}: |
The population proportions are not p _{A} = 0.2 , p _{B} = 0.4 , and p _{C} = 0.4 |
A sample of size 200 yielded 40 in category A, 120 in category B, and 40 in category C. Use = .01 and test to see whether the proportions are as stated in H_{0}. Use Table 12.4. a. Use the p-value approach. χ ^{2} = (to 2 decimals) The p-value is Select less than .005 between .005 and .01 between .01 and .025 between .025 and .05 between .05 and .10 greater than .10Item 2 Conclusion: Conclude the proportions differ from 0.2, 0.4, and 0.4. Cannot conclude that the proportions differ from 0.2, 0.4, and 0.4.Item 3 b. Repeat the test using the critical value approach. χ ^{2} _{.01} = (to 3 decimals) Conclusion: Conclude the proportions differ from 0.2, 0.4, and 0.4. Cannot conclude that the proportions differ from 0.2, 0.4, and 0.4.Item 5 |
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