# Chi-Square Test for Proportions

The Chi-Square test for proportions is illustrated using the following example.

During the first 13 weeks of the television season, the Saturday evening 8:00 p.m. to 9:00 p.m. audience proportions were recorded as ABC 29%, CBS 28%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 95 homes, CBS 70 homes, NBC 89 homes, and independents 46 homes.

Test with a= 0.05 to determine whether the viewing audience proportions changed.

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#### Solution Preview

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The Chi-Square test for proportions is illustrated using the p-value approach and traditional approach.

Solution

The null and alternative hypotheses are

H0: pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18

Ha: The proportions are not pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18

The test statistic is given by,

(please see ...

#### Solution Summary

In this solution a chi-square test is used to determine whether there was a change in proportions.