An article gave the following summary information for fractu

An article gave the following summary information for fracture strengths (MPa) of n = 144 ceramic bars fired in a particular kiln: x = 68.54, s = 3.81.

(a) Suppose the investigators had believed a priori that the population standard deviation was about 6 MPa. Based on this supposition, how large a sample would have been required to estimate to within 0.5 MPa with 95% confidence?

Solution

we have

error = Z * sigma / srqt (n)

n = [ ( Z * sigma ) / error ] ^2

for alpha = 0.05

alpha / 2 = 0.025

Z = 1.96

n = [ (1.96 * 6 ) / 0.5 ] ^2

n =553.1904

n = 554