Question

A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard deviation σ=30 hours. Find the sample size needed so that a 90% confidence interval for the mean lifetime will have a margin of error of 7.

Answer 1

Solution :

Given that,

standard deviation =s =   =30

Margin of error = E = 7

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

n = ( 1.645 * 30 / 7 )2

n =49.7025

Sample size = n =50