889 randomly selected US adults, were asked if they believed in ghosts, 29% said they did.

(a) In constructing confidence intervals, would z or t be used in this situation? explain why you would use one instead of the other.

(b) Estimate p, the true proportion of US adults that believe in ghosts, with 90% confidence. Interpret the interval in context of the data.

(c) Suppose, using the information from the survey (the 29% that believe in ghosts) that a new survey is to be taken and the new bound is to be 2%. What sample size will be required?

(d) Suppose there is no estimate for the proportion of those US adults that believe in ghosts. What proportion should be used for the estimation? What sample size do we need with no prior information? Why is it different than the sample size from part (c)?