Question

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. From research on other college​ campuses, you believe the proportion will be near 3030​%. What sample size is needed if you wish to be 9999​% confident that your estimate is within 0.020.02 of the true​ proportion?

Answer 1

3484

Explanation:

The following formula is used to compute the minimum sample size required to estimate the population proportion within the required margin of error:

n≥ p×(1-p) ×
`((z)/(ME) )^2` where

• n is the sample size
• p is the proportion of traditional college students who own their own car
• z is the corresponding z-score for 99% confidence level
• ME is the margin of error in the estimation

we have p=0.30 (30%) z=2.58 ME= 0.02 then we get

n≥ 0.3×(1-0.3) ×
`((2.58)/(0.02) )^2` = 3483.32

therefore we need at least 3484 students under these conditions.