A social service agency plans to conduct a survey to determine the mean income o

Question

A social service agency plans to conduct a survey to determine the mean income of its clients. The director of the agency prefers that you measure the mean income very accurately, to within +-$500. From a sample taken 2 years ago, you estimate that the standard deviation of income for this population is about $5,000. Your job is to figure out the necessary sample size to reduce sampling error to +- $500

a)Do you need to have an estimate of the current mean income to answer this question? Why or why not?

b)What sample size should be drawn to meet the director’s requirement at the 95% level of confidence? (Hint: Use the formula for a confidence interval and solve for N, the sample size.)

c)What sample size should be drawn to meet the director’s requirement at the 99% level of confidence?

Explanation / Answer

Solution:

a) No, because we know the error (difference between the true mean and the estimated mean to be 500)

b) The z-value for a 95% confidence interval is 1.96
N = [ z sd / error]^2
N = [ (1.96)(5000) / 500] ^2
N = 384.16
N = 385

c)
The z-value for a 99% confidence interval is 2.575
N = [ z sd / error]^2
N = [ (2.575)(5000) / 500] ^2
N = 663.06
N = 664

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.