In: Statistics and Probability
A research group conducted an extensive survey of 2922 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?" 1466 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 2.0% of the population percentage?
(Hint: Use p ≈ 0.50 as a preliminary estimate.
Round your answer up to the nearest whole number.)
workers
Solution,
Given that,
= 0.50
1 - = 1 - 0.50 = 0.50
margin of error = E = 2.0% = 0.02
At 95% confidence level
= 1 - 95%
= 1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.96
sample size = n = (Z / 2 / E )2 * * (1 - )
= (1.96 / 0.02)2 * 0.50 * 0.50
= 2401
sample size = n = 2401