A sample of 10 observations is selected from a normal popula

A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 3. The sample mean is 20. (Round your answers to 3 decimal places.)

The 99 percent confidence interval for the population mean is between  and .

Solution

(a) The standard error of the mean is

s/vn =3/sqrt(10) =0.949

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(b) The degree of freedom =n-1=10-1=9

Given a=1-0.99=0.01, t(0.005, df=9) =3.25 (from student t table)

So the lower bound is

xbar - t*s/vn = 20-3.25*0.949 =16.916

So the upper bound is

xbar +t*s/vn =20+3.25*0.949=23.084