Airline companies recognize that empty seats represent lost revenues that can never be recovered. To avoid losing revenues, the companies often book more passengers than there are available seats. Then, when a flight experiences fewer no shows than expected, some passengers are “ bumped” from their flights ( are denied boarding). Incentives are provided to encourage passengers to give up their reserved seat voluntarily, but occasionally some passengers are involuntarily bumped from the flight. Obviously, these incidents can reflect poorly on customer satisfaction. Suppose Southwest Airlines would like to estimate the true proportion of involuntarily bumped passengers across all domestic flights in the industry. In a pilot sample of 55 domestic passengers, 5 were involuntarily bumped from their flights.

a. Determine the sample size needed to construct a 98% confidence interval with a margin of error no more than 5% to estimate the true proportion of involuntarily bumped passengers.

b. Verify your result using PHStat.