A sample of 12 observations taken from a normal distribution

A sample of 12 observations taken from a normal distribution produced the following data: 13, 15, 9, 11, 8, 16, 14, 9, 10, 16, 12. Construct the 95% confidence interval for M.

Solution

First find mean and std deviation for the given sample of 11 observations.

13, 15, 9, 11, 8, 16, 14, 9, 10, 16, 12

Mean =12.091

sd = 2.778

Margin of error for 95% = 1.96 *(2.778/rt 11) = ±1.64

Hence confidence interval = (10.45 , 13.73)