Aim: To find the confidence interval of the population mean when the variance is known.
Problem:-
A machine produces components, which have a standard deviation of 1.6cm in length. A
random sample of 64 parts is selected from the output and this sample has a mean length of
90cm. The customer will reject the part if it is either less than 88cm or more than 92cm. Does
the 95% confidence interval for the true mean length of all the components produced ensure
acceptance by the customer?
R- Code:-
>n=64
>sigma=1.6
>xbar=90
>sem=sigma / sqrt(n);sem
[1] 0.2
>E=qnorm(0.975)*sem;E
[1] 0.3919928
>xbar+c(-E,E)
[1] 89.081 90.39199