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 22 HOURS.

FIND THE SAMPLE SIZE NEEDED SO THAT 90% CONFIDENCE INTERVAL FOR THE MEAN LIFETIME WILL HAVE A MARGIN OF ERROR OF 8.

Answer 1

Solution =

Given ,

= 22 ..Population SD

E = 8 Margin of error

c = 90% = 0.90 ...confidence level

Find sample size required.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.05

Using Z table ,

= 1.645   

Now, sample size (n) is given by,

=  {(1.645 * 22 ) / 8 }2

= 20.4643

= 21 ..(round to the next whole number)

Answer : Required Sample size is n = 21