The National Study of the Changing Workforce conducted an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sampe. In repsonse to the question "What does success mean to you?" 1538 responded "Personal satification from doing a good job." Let p for the population of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p.

How large of a sample is needed if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1% of the poulation percentage?

HINT: Use p = 0.52 as a preliminary estimate.