What sample size would be required to detect a true mean dia

What sample size would be required to detect a true mean diameter as low as 1.495 inches if we wanted the power of the test to be at least 0.88?

Solution

power of the test = 0.88

=> 1-beta = 0.88 => beta = 0.12

alpha = 0.01

required sample size = [Z(alpha/2) + Z(beta)]^2 * sigma^2/delta^2

= [2.58 + 1.175]^2 * 0.01^2 / (1.5-1.4975)^2

= 225.6
= 226 ....................ans