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 23%, and independents 20%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 93 homes, CBS 67 homes, NBC 82 homes, and independents 58 homes. Test with a = .05 to determine whether the viewing audience proportions changed. Use Table 12.4. Round your answers to two decimal places. 6.41

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**Analysis of Television Audience Proportions**

During the first 13 weeks of the television season, the audience proportions for Saturday evening (8:00 P.M. to 9:00 P.M.) were as follows:
- ABC: 29%
- CBS: 28%
- NBC: 23%
- Independents: 20%

A sample of 300 homes was taken two weeks after a Saturday night schedule revision, resulting in the following viewing audience data:
- ABC: 93 homes
- CBS: 67 homes
- NBC: 82 homes
- Independents: 58 homes

**Statistical Test for Change in Audience Proportions**

A chi-square test was conducted with a significance level (\(\alpha\)) of 0.05 to determine whether the viewing audience proportions had changed.

- Calculated \(\chi^2\) value: **6.41**
- p-value is between **0.05 and 0.10**

**Conclusion**

Based on the test results, there is no significant change in the viewing audience proportions. The differences observed in the sample do not provide sufficient evidence to suggest a change from the original proportions.
Transcribed Image Text:**Analysis of Television Audience Proportions** During the first 13 weeks of the television season, the audience proportions for Saturday evening (8:00 P.M. to 9:00 P.M.) were as follows: - ABC: 29% - CBS: 28% - NBC: 23% - Independents: 20% A sample of 300 homes was taken two weeks after a Saturday night schedule revision, resulting in the following viewing audience data: - ABC: 93 homes - CBS: 67 homes - NBC: 82 homes - Independents: 58 homes **Statistical Test for Change in Audience Proportions** A chi-square test was conducted with a significance level (\(\alpha\)) of 0.05 to determine whether the viewing audience proportions had changed. - Calculated \(\chi^2\) value: **6.41** - p-value is between **0.05 and 0.10** **Conclusion** Based on the test results, there is no significant change in the viewing audience proportions. The differences observed in the sample do not provide sufficient evidence to suggest a change from the original proportions.
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