Construct confidence interval for population


A random sample of size n=100 is taken from the population with σ=5.1 .Given that the sample mean is =21.6,construct a 95% confidence interval for the population mean μ.


given mean {\displaystyle {\bar {x}}} {\bar {x}}=21.6
and given that n=100 here n is no.of samples
let us assume standard devaition as s
so given s=5.1
so formula for calculating interval is
( {\displaystyle {\bar {x}}} {\bar {x}}-z{\displayable{\sub{σ/2}}}.σ/√n ,{\displaystyle {\bar {x}}} +z{\displayable{\sub{σ/2}}}.σ/√n)
for 95% of level of significance z{\displayable{\subscript{σ/2}}}=1.96
now z{\displayable{\sub{σ/2}}}.σ/√n=1.96*5.1/√100=0.9996
now {\displaystyle {\bar {x}}} {\bar {x}}-z{\displayable{\subscript{σ/2}}}.σ/√n=21.6-0.9996=20.6004
now \displaystyle {\bar {x}}} +z{\displayable{\subscript{σ/2}}}.σ/√n)=21.6+0.9996=22.5996

hence at 95% levelof significance the confidence interval for given population is (20.6004,22.5996)