3 suppose you want to test a claim about a proportion and wa

3. suppose you want to test a claim about a proportion, and want the margin of error to be 0.05 with level of significance = .10. Determine the sample size that is required.(There is no estimated value for p.hat)

Solution

Standard of Deviation — How much variance do expect is responses. till haven’t actually administered our survey yet, the safe decision is to use 0.5 – this is the most forgiving number and ensures that your sample will be large enough.

Here are the z-scores for the most common confidence levels:

90% – Z Score = 1.645

Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²

= (1.645)² * 0.5*(1-0.5) / (0.05)²

=2.706*0.5(0.5) / (0.05)²

=0.6765 / (0.05)²

=270.6

The sample size is 271.