Stats Help Math Problem?

Question

If you want to find the percentage of people who are left-handed, how many people must we survey in order to be 99% confident that we are within 3 percentage points of the population percentage? Assume that we know nothing about the percentage of the population that is left-handed

Answer 1

To determine the sample size needed to estimate the percentage of left-handed people with a 99% confidence level and a margin of error of 3 percentage points, you can use the formula for sample size calculation:

n = (Z².p(1-p))/E²

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level (for 99% confidence level, Z is approximately 2.576)

p is the estimated proportion of the population that is left-handed (since we don't know this, we can use p =0.5 for maximum variability)

E is the desired margin of error (3 percentage points, so E =0.03)

Plugging in the values:

n = ((2.576)²0.5(1-0.5))/(0.03)²

​

≈1776.52

So, you would need to survey around 1777 people in order to be 99% confident that your estimate of the percentage of left-handed people is within 3 percentage points of the population percentage.