Question

It is known that the diameters of the rods of an aluminum alloy produced in an extrusion machine have a standard deviation of 0.0001 inches. A random sample of 38 rods with an average diameter of 0.5046 inches. It can be assumed that the actual mean diameter of the rods is 0.5025 inches, use a confidence interval of 99% to conclude.

Answer 1

Sol:

population standard deviation=0.0001

sample szie=n=38,n>30

given sample is large sample

Z crit for 99%=2.576

sample mean=xbar=0.5025

99% confidenc einterval for true mean diameter of rods is

xbar-z*popsd/sqrt(n),xbar+z*popsd/sqrt(n)

0.5046 -2.576*0.0001/sqrt(38),0.5046 +2.576*0.0001/sqrt(38)

0.5046,0.5046

it cannot be assumed that the actual mean diameter of the rods is 0.5025 inches

because it is not in the 99% confidence interval for the true mean diameters of the rods of an aluminum alloy produced in an extrusion machine .