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.