The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this portion is within 3% of the true proportion. How large a sample is necessary?

Answer 1

Try this formula:
n = [(z-value)^2 * p * q]/E^2
= [(2.33)^2 * .8 * .2]/.03^2

I'll let you finish the calculation. Round to the next highest whole number.

Note: n = sample size needed; .8 for p and .2 for q (q = 1 - p). E = maximum error, which is .03 (3%) in the problem. Z-value is found using a z-table (for 98%, the value is approximately 2.33).

I hope this will help.