You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately $\sigma=24.7$. You would like to be $95 \%$ confident that your estimate is within 10 of the true population mean. How large of a sample size is required?
Hint: Video 구 [+]
\[
n=
\]
Answer
Calculating the above expression, we find that the required sample size is \(\boxed{24}\).
Step 1 ：We are given that the population standard deviation (\(\sigma\)) is 24.7, the desired margin of error (E) is 10, and the Z-score (Z) for a 95% confidence level is 1.96.
Step 2 ：We need to find the sample size (n) using the formula: \(n = (Z*\sigma/E)^2\)
Step 3 ：Substituting the given values into the formula, we get: \(n = (1.96*24.7/10)^2\)
Step 4 ：Calculating the above expression, we find that the required sample size is \(\boxed{24}\).
