Question

Determine the margin of error for a confidence interval to estimate the population mean with n=18 and s=12.3 for the confidence levels below

a) 80%
b) 90%
c) 99%

Answer 1

To determine the margin of error for a confidence interval, we use the formula: Margin of Error = z * (s / √(n)). The margin of error for a) 80% confidence level is 2.620, b) 90% confidence level is 3.298, and c) 99% confidence level is approximately 5.161.

Step-by-step explanation:

To determine the margin of error for a confidence interval, we use the formula:
Margin of Error = z * (s / √(n))
where z is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.

a) For an 80% confidence level:
Using the z-score for an 80% confidence level (z = 1.282), the margin of error is:
Marggin of Error = 1.282 * (12.3 / √(18))
Marggin of Error ≈ 2.620

b) For a 90% confidence level:
Using the z-score for a 90% confidence level (z = 1.645), the margin of error is:
Marggin of Error = 1.645 * (12.3 / √(18))
Marggin of Error ≈ 3.298

c) For a 99% confidence level:
Using the z-score for a 99% confidence level (z = 2.576), the margin of error is:
Marggin of Error = 2.576 * (12.3 / √(18))
Marggin of Error ≈ 5.161