Problem
Suppose your boss wants you to obtain a sample to estimate a population mean. Based on previous analyses, you estimate that 41 is the approximate value of the population standard deviation. You would like to be $98 \%$ confident that your estimate is within 34 of the true population mean. What is the minimum sample size required? IMPORTANT: Use a critical value that you found with your calculator (not from a table), and round it to $\underline{3}$ places after the decimal point before you plug it into a formula and perform your calculations. Do not round-off any other intermediate results.
Solution
Step 1 ：Given that the standard deviation (σ) is 41, the desired margin of error (E) is 34, and the z-score (Z) for a 98% confidence level is approximately 2.326.
Step 2 ：The formula for determining the sample size (n) is given by: \(n = (Z*σ/E)^2\).
Step 3 ：Substitute the given values into the formula: \(n = (2.326*41/34)^2\).
Step 4 ：Calculate the value of n.
Step 5 ：Round the value of n to the nearest whole number, because the sample size must be a whole number.
Step 6 ：Final Answer: The minimum sample size required is \(\boxed{8}\).
