In a recent poll, YouGov asked Americans about their belief in various paranormal entities. Based on a sample of 1000 Americans, 480 indicated that they believe that ghosts, demons, and other supernatural beings do exist.
a. Develop an 92% confidence interval for the proportion of Americans that believe in the supernatural beings.
b. Is it reasonable to assume that more than 50% of Americans believe in the existence of supernatural beings? Why or why not?
c. If YouGov wanted to minimize the cost of the study, how many subjects would they optimally survey? Assume that he wants a 95% level of confidence and the error is to be within 10%.