you are to estimate the mean thickness of lenses produced fo

you are to estimate the mean thickness of lenses produced for binoculars. A sample of 22 lenses reveals a mean of .54mm with a standard diviation of .14mm. Whats is the point estimate? Construct a 99% confidence interval.

Solution

given n=22 ,X^=054 sigma=0.14

we know that Z=(x-mu)/(sigma/sqrt(n))

for 99% confidence level Z=2.58

therefore from the above test statistic we can find mean mu=X^-(z*(sigma/sqrt(n)))=0.462

Margin of error=z*(sigma/sqrt(n))=0.077

99% confidence interval=X+-MOE

X+MOE=0.54+0.077=0.617----->Upper limit

X-MOE=0.54-0.077=0.463--------> Lower limit