The Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To test a new campaign, they recently sent letters to a random sample of 100,000 potential donors and received 4781 donations.
a) Give a 95% confidence interval for the true proportion of their entire mailing list who may donate.
b) A staff member thinks that the true rate is 5%. Given the confidence interval you found, do you find that percentage plausible?