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# Statement of a problem № m40185

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A Newsweek article titled “America the Ignorant” (www.newsweek.com) described a Gallup poll that asked adult Americans if they believe that there are real witches and warlocks. Suppose that the poll used a random sample of 800 adult Americans and that you want to use the poll data to decide if there is evidence that more than 10% of adult Americans believe in witches and warlocks. Let p be the proportion of all adult Americans who believe in witches and warlocks. a. Describe the shape, center, and spread of the sampling distribution of  for random samples of size 800 if the null hypothesis H0: p = 0.10 is true. b. Would you be surprised to observe a sample proportion of  = 0.16 for a sample of size 800 if the null hypothesis H0: p = 0.10 were true? Explain why or why not. c. Would you be surprised to observe a sample proportion of  = 0.12 for a sample of size 800 if the null hypothesis H0: p = 0.10 were true? Explain why or why not. d. The actual sample proportion observed in the study was  = 0.21. Based on this sample proportion, is there convincing evidence that more than 10% of adult Americans believe in witches and warlocks, or is the sample proportion consistent with what you would expect to see when the null hypothesis is true? Support your answer with a probability calculation.

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