Question

A research group conducted an extensive survey of 3108 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?" 1639 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 2.6% of the population percentage? (Hint: Use p ≈ 0.53 as a preliminary estimate. Round your answer up to the nearest whole number.)

Answer 1

Estimated p : sample proportion of those equating success with personal satisfaction = 1639/3108=0.53

Formula for sample size: n while estimating confidence interval for proportion

Given,

95% confident that the sample percentage of those equating success with personal satisfaction is within 2.6% of the population percentage i.e

E: Margin of error = 2.6/100=0.026

for 95% confidence level = (100-95)/100 =0.05

/2 =0.05/2=0.025

Z/2 = Z0.025 = 1.96

Sample size = 1416

Sample of 1416 is needed if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 2.6% of the population percentage