Question

Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed.

c=0.95, x=12.2​, s=0.85​, n=15

Answer 1

Solution:

Given:   the population is normally distributed. We have to construct the indicated confidence interval for the population mean μ using the​ t-distribution.

c = 0.95, ​, s = 0.85​, n = 15

Formula:

where

t_c is t critical value for c = 95%  confidence level

Thus two tail area = 1 - c = 1 - 0.95 = 0.05

df = n - 1 =  15 - 1 = 14

Look in  t table for df = 14 and two tail area = 0.05 and find t critical value.

t_c = 2.145

Thus

Thus

Thus we are 95% confident that the true population mean μ is between ( 11.73 , 12.67 )