In the last presidential election, before the candidates started their major campaigns, the percentages of registered voters who favored the various candidates were as follows.
?
Percentages
Republicans34%
Democrats43%
Independents23%
?
?
?
?
?
After the major campaigns began, a random sample of 400 voters showed that 172 favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64 favored the Independent candidate. We are interested in determining whether the proportion of voters who favored the various candidates had changed.
?
a.
Compute the test statistic.b.
Using the p-value approach, test to see if the proportions have changed. Let ? = .05.c.
Using the critical value approach, test the hypotheses. Use ? = .05.
What will be an ideal response?
| a. | ?2 = 18.42 |
| b. | p-value < .005, reject H0; the proportions have changed. |
| c. | ?2 = 18.42 > 5.991; reject H0; the proportions have changed. |
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