Question 574039: A new television series must show that it has at least 25% of the viewing audience after its initial 13- week run, in order to be judged successful. In a sample of 400 households, 112 were watching the series. At a 5% significance level, would the series be judged successful on the basis of this sample information?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A new television series must show that it has at least 25% of the viewing audience after its initial 13- week run, in order to be judged successful. In a sample of 400 households, 112 were watching the series. At a 5% significance level, would the series be judged successful on the basis of this sample information?
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Ho: p >= 0.25
Ha: p < 0.25
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sample proportion: p-hat = (112/400) = 0.28
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z(0.28) = (0.28-0.25)/sqrt[0.25*0.75/400] = 1.3856
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p-value = P(z > 1.3856) = normalcdf(1.3856,100) = 0.0829
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Conclusion: since the p-value > 5%, fail to reject Ho.
The test results support the success of the TV series.
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Cheers,
Stan H.
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