Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe

the population proportion is approximately 40 %. You would like to be 90% confident that your estimate is
within 4.5% of the true population proportion. How large of a sample size is required?

n=

Answer 1

To estimate a population proportion with a desired level of confidence and margin of error, we can use the formula for sample size. In this case, a sample size of at least 384 is required to obtain a 90% confidence level with a margin of error of 4.5%.

Step-by-step explanation:

To estimate a population proportion with a desired level of confidence and margin of error, we can use the formula for sample size:

n = (z² * p' * q') / EBP²

Where:

• n = sample size
• z = z-score corresponding to the desired level of confidence
• p' = estimated population proportion
• q' = 1 - p' (complement of the estimated population proportion)
• EBP = margin of error

In this case, we want to estimate the population proportion with a 90% confidence level and a margin of error of 4.5%. We estimate the population proportion to be 40%. Plugging these values into the formula:

n = ((1.645² * 0.4 * 0.6) / 0.045²)

n ≈ 384

Therefore, a sample size of at least 384 is required to obtain a 90% confidence level with a margin of error of 4.5%.