SOLUTION: 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,

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 Click here to see ALL problems on Probability-and-statistics 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(57205)   (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? ----- Ho: p >= 0.25 Ha: p < 0.25 ------------------------- sample proportion: p-hat = (112/400) = 0.28 ------ z(0.28) = (0.28-0.25)/sqrt[0.25*0.75/400] = 1.3856 ---- p-value = P(z > 1.3856) = normalcdf(1.3856,100) = 0.0829 ---- Conclusion: since the p-value > 5%, fail to reject Ho. The test results support the success of the TV series. =================== Cheers, Stan H. =============