Question

The average thickness of a flange on an aircraft component is found to be 1 mm (from a sample of 36 measurements). a) Find the 95% and 99% confidence intervals for the mean thickness. Assume the population standard deviation is 0.1 mm. b) If we want to be 95% confident that our estimate of µ is off by less than 0.02 mm, how large of a sample is required?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 1 mm

Population standard deviation =    = 0.1 mm

Sample size = n = 36

a) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 0.1 /  36 )

= 0.03

At 95% confidence interval estimate of the population mean is,

  ± E

1 ± 0.03   

( 0.97mm, 1.03 mm )  

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 0.1 /  36 )

= 0.04

At 99% confidence interval estimate of the population mean is,

  ± E

1 ± 0.04   

( 0.96mm, 1.04 mm )  

b) Margin of error = E = 0.02 mm

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96  

sample size = n = [Z/2* / E] 2

n = [1.96 * 0.1/ 0.02 ]2

n = 96.04

Sample size = n = 97