Question

A research group conducted an extensive survey of 3170 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 sample. In response to the question, "What does success mean to you?" 1454 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. How large a sample is needed if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1.8% of the population percentage? (Hint: Use p ≈ 0.46 as a preliminary estimate. Round your answer up to the nearest whole number.)

workers

Answer 1

Given,

p = 0.46, q = 1 - p = 1 - 0.46 = 0.54

For 95% confidence, z = 1.96

E = 0.018

Hence,

Sample size

n = 2946