Question

A random sample is drawn from a population of known standard deviation 11.3. Construct a 90% confidence interval for the population mean based on the information given (not all of the information given need be used).

a. n = 36, x-=105.2, s = 11.2

b. n = 100, x-=105.2, s = 11.2

Answer 1

a.

$90\%CI=(\bar x-1.645\frac{s}{\sqrt{n}},\;\bar x+1.645\frac{s}{\sqrt{n}})=\\ =(105.2-1.645\frac{11.2}{\sqrt{36}},\;105.2+1.645\frac{11.2}{\sqrt{36}})=\\ =(102.13,\;108.27).$

b.

$90\%CI=(\bar x-1.645\frac{s}{\sqrt{n}},\;\bar x+1.645\frac{s}{\sqrt{n}})=\\ =(105.2-1.645\frac{11.2}{\sqrt{100}},\;105.2+1.645\frac{11.2}{\sqrt{100}})=\\ =(103.36,\;107.04).$