Question

Suppose that you plan to conduct an SRS of adults in the U.S., age 50 to 65, who have not yet retired. You plan to ask how much each adult has saved for retirement. Suppose that the standard deviation for amount saved for retirement is $21,161. Your desired margin of error for a 95% confidence interval is $1,000. What is the smallest sample size that you need to acheive this margin of error with 95% confidence? In your calculation, use the appropriate critical value z* appropriate for a 95% confidence interval.

Round up to the nearest integer value. Note: be careful not to round at intermediate steps in your calculation.

Answer 1

Solution :

Given that,

Population standard deviation = = 21,161

Margin of error = E = 1,000

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 *21,161 / 1,000 ]²

n = 1720.22

Sample size = n = 1721