Question

You want to obtain a sample to estimate the proportion in the population who support gun control.

Based on previous evidence, you believe the population proportion is approximately 15%. You
would like to be 90% confident that your estimate is within 0.5% of the true population proportion.
How large of a sample size is required?
Do not round mid-calculation. However, use a critical value accurate to three decimal places.
n=

Answer 1

n = 9870

Explanation:

To determine the required sample size, we need to use the following formula:

n = (z^2 * p * q) / E^2

where:

n is the sample size

z is the z-score associated with the desired level of confidence

p is the estimated population proportion

q is 1 - p (the complement of the population proportion)

E is the maximum error of the estimate

In this case, we want to be 90% confident that our estimate is within 0.5% of the true population proportion, so we have:

z = 1.645 (from the standard normal distribution table for a 90% confidence level)

p = 0.15

q = 1 - 0.15 = 0.85

E = 0.005

Substituting these values into the formula, we get:

n = (1.645^2 * 0.15 * 0.85) / 0.005^2

Solving for n, we get:

n = 9869.795

Since we cannot have a fractional number of individuals in our sample, we need to round up to the nearest whole number. Therefore, the required sample size is:

n = 9870