You wish to estimate, with 95% confidence, the population proportion of U.S. adults who have taken or planned to take a winter vacation in a recent year. Your estimate must be accurate within 5% of the population proportion. 

(a) No preliminary estimate is available. Find the minimum sample size needed. 

(b) Find the minimum sample size needed, using a prior study that found that 32% of U.S. adults have taken or planned to take a winter vacation in a recent year.  

(c) Compare the results from parts (a) and (b).