Question

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. You have no preconceived idea of what that proportion might be. What sample size is needed if you wish to be 90​% confident that your estimate is within 0.03 of the true​ proportion? A sample size of nothing is needed.

Answer 1

Solution:

Given ,

Margin of error E = 0.03

Confidence level c = 90% = 0.90

You have no preconceived idea of what that proportion might be.

In this case , take p = 0.5

Now,

= 1 - c = 1 - 0.90 = 0.10

/2 = 0.05

= 1.645 (using z table)

The sample size for estimating the proportion is given by

n =

= (1.645)² * 0.5 * 0.5 / (0.03²)

= 751.673611111

= 752 ..(round to the next whole number)

Answer :

A sample size of 752 is needed.