As part of your job as Alumni President, you are interested in finding information about graduates and jobs. You are planning to conduct a study whereby you will be able to estimate the average annual salary of all graduates who continue to work for the same company they originally joined upon graduation. A telephone survey is planned. In order to conduct the sample design, you conduct a quick convenience survey of only 30 graduates that you know and find that 4 out of 10 are still with the first company they joined after graduation, their average salary is $65,000, and 29 out of the 30 respondents indicated their salary was between $55,000 and $75,000.

a) What size random sample should you take if you want to estimate the annual salary in the population with 99 percent confidence and a maximum margin of error of $250?

b) A fellow researcher tells you that the response rate on your telephone survey is likely to be 80%. Thus, how many alumni should you pick from the sample frame and then proceed to call.