Question

A new method of pre-coating fittings used in oil, brake, and other fluid systems in heavy-duty trucks is being studied. How large a sample is needed to estimate the proportion of fittings that leak to within 2% with 90% confidence?

Please explain how to find the sample size from just percent confidence and (margin of error?)

Answer 1

Solution :

Given that,

= 0.5 ( when estimate is not given then use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E = 2% = 0.02

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645 ( using standard normal table)

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.645/ 0.02)² * 0.5 * 0.5

= 1691.26 = 1691

Sample size = 1691