Question

A team of researchers are developing a prosthetic hand that can sense the elasticity of objects. To test the accuracy of their sensors, they plan to conduct a series of tests where they measure objects with known elasticity. Each data point is the difference between the measurement and the known elasticity, i.e.. the the measurement errors. Suppose the population standard deviation across such measurement errors is 0.8 GPa. The researchers wish to conduct a fixed level test with significance 0.015 and 85% power to detect a measurement error as small as 0.25 GPa. What is the smallest number of measurements they should take?

Answer 1

answer

given that

standard deviation = 0.8

difference = 0.25

z(beta) score = 1.04 (for 85% power)

z(alpha/2) score = 2.43

sample size n =

(a/228)21/d2 - [ (0.8)2 (2.43+ 1.04)21/0.25- - 7.71/0.0625 -123.3 = 124

Sample size n = 124 (rounded to next integer)