Question 7 2 pts (CO 4) Determine the minimum sample size required when you want to be $80 \%$ confident that the sample mean is within 1.3 units of the population mean. Assume a standard deviation of 9.24 in a normally distributed population. 84 195 83 194
Solution
Step 1 ：The question is asking for the minimum sample size required to be 80% confident that the sample mean is within 1.3 units of the population mean. The standard deviation is given as 9.24.
Step 2 ：We can use the formula for the sample size in a confidence interval estimation for a population mean: \(n = (Z*σ/E)^2\) where: n is the sample size, Z is the Z-score (which corresponds to the desired confidence level), σ is the standard deviation of the population, E is the desired margin of error.
Step 3 ：For a confidence level of 80%, the Z-score is approximately 1.28 (you can find this value in a standard Z-table or use a statistical calculator).
Step 4 ：Let's plug the values into the formula and calculate the sample size. Z = 1.28, sigma = 9.24, E = 1.3, n = 83.
Step 5 ：The calculation gives us the minimum sample size required to be 80% confident that the sample mean is within 1.3 units of the population mean, given a standard deviation of 9.24. The result is 83.
Step 6 ：Final Answer: The minimum sample size required is \(\boxed{83}\).
