Question

14. Use the given degree of confidence and Sample data to construct a confidence interval for the population mean. Assume that the population has a normal distribution.

n=10, x=8.7, s=3.3, 95% confidence
I know the answer is 6.34<μ<11.06 but I dont know how to get there

Answer 1

Explanation:

Confidence interval = mean ± margin of error

CI = μ ± ME

The mean is μ = 8.7.

Margin of error = critical value × standard error

ME = CV × SE

At 95% confidence and 9 degrees of freedom, CV = 2.262.

SE = s / √n

SE = 3.3 / √10

SE = 1.04

The margin of error is:

ME = 2.262 × 1.04

ME = 2.36

CI = 8.7 ± 2.36

CI = (6.34, 11.06)