Question

A research group conducted an extensive survey of 3077 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?" 1629 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 1.1% of the population percentage? (Hint: Use p ≈ 0.53 as a preliminary estimate. Round your answer up to the nearest whole number.)

Answer 1

Solution:

Given,

E = 1.1% = 0.011

c = 95% = 0.95

p = 0.53

1- p = 1 - 0.53 = 0.47

Now,

  = 1 - c = 1 - 0.95 = 0.05

/2 = 0.025

= 1.96

The sample size for estimating the proportion is given by

n =

= (1.96)² * 0.53 * 0.47 / (0.011²)

= 7908.61619835

= 7909 ..(round to the next whole number)

Answer : Sample size needed is 7909