A sample of 12 measurements of the breaking strengths of cot

A sample of 12 measurements of the breaking strengths of cotton threads gave a mean of 7.38 oz and a standard deviation of s=1.24 oz. Find the bounds of the 95% confidence interval for the actual mean breaking strength.

6.59 ?

Solution

The degree of freedom =n-1=12-1=11

Given a=1-0.95=0.05, t(0.025, df=11) =2.2 (from student t table)

So the lower bound is

xbar - t*s/vn =7.38 -2.2*1.24/sqrt(12) =6.592494

So the upper bound is

xbar + t*s/vn =7.38 +2.2*1.24/sqrt(12) =8.167506

Answer: 6.59 ?