SOLUTION: For many years TV executives used the guideline that 30 percent of the audience were watching each of the traditional big three prime-time networks and 10 percent were watching cab

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Question 245994: For many years TV executives used the guideline that 30 percent of the audience were watching each of the traditional big three prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 550 viewers in the Tampa–St. Petersburg, Florida, area last Monday night showed that 175 homes were tuned in to the ABC affiliate, 170 to the CBS affiliate, 165 to the NBC affiliate, and the remainder were viewing a cable station. At the 0.1 significance level, can we conclude that the guideline is still reasonable?
Answer by stanbon(75887) About Me  (Show Source):
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For many years TV executives used the guideline that 30 percent of the audience were watching each of the traditional big three prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 550 viewers in the Tampa–St. Petersburg, Florida, area last Monday night showed that 175 homes were tuned in to the ABC affiliate, 170 to the CBS affiliate, 165 to the NBC affiliate, and the remainder were viewing a cable station. At the 0.1 significance level, can we conclude that the guideline is still reasonable?
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Network numbers are 175+170+165 = 510
Proportion is 510/550 = 0.9273
Cable numbers are 550-510 = 40
Proportion is 40/550 = 0.0727
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It's a Goodness-of-Fit problem.
Expected values are 0.30--------------0.10
Observed values are 0.9273-----------0.0727
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Express the comparison in whole numbers:
Expected values---3000-----------1000
Observed values---9273------------727
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Ho: The proportions are the same
H1: At least one of the proportions is different
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Run a Chi-Sq. Goodness of Fit program on the two rows of data:
I got the following:
Chi-Sq = 4346.08
p-value is 0 to 4 decimal places
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Conclusion: Reject Ho; These test results support
the conclusion that the guidelines should be changed.
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Cheers,
Stan H.