Statistics Homework

Question

You want to obtain a sample to estimate the proportion of a population that possess a particular genetic marker. Based on previous evidence, you believe approximately p∗=42%p∗=42% of the population have the genetic marker. You would like to be 90% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required?

n = 

Do not round mid-calculation. However, you may use a critical value accurate to three decimal places.

Answer 1

In order to solve this problem, you need to use the minimum sample size formula. Illustrated below is the specific formula.

n = (Z² * (P * (1 - P)))/ E²

In the problem specifically,

Z score = 1.645 (90% confidence level yields a z-score of 1.645)

P = 0.42

E = 0.03

Therefore, the minimum sample required is

n = (1.645² * (0.42 * (1 - 0.42)))/ 0.03² = 732.24

Since subjects need to be whole numbers we must round up to get an answer of:

n = 733