How much does a sleeping bag cost Twenty bags were examined

How much does a sleeping bag cost? Twenty bags were examined and the average price was mean = $83.75 and s = $ 28.97. Use this information to find 90% confidence interval for the mean price of all sleeping bags. What does the confidence interval mean in the context of this problem?

(Show all work and all formulas)

Solution

The degree of freedom =n-1=20-1=19

Given a=1-0.9=0.1, t(0.05, df=19) = 1.729 (from student t table)

So the lower bound is

xbar - t*s/vn=83.75 - 1.729*28.97/sqrt(20) =72.54973

So the upper bound is

xbar + t*s/vn =83.75 + 1.729*28.97/sqrt(20)=94.95027

We have 90% confident that the population mean will be within this interval.