Question

(d) A similar study was conducted on salary distribution of Paris residents in 2019. The research team aimed to estimate the average salary. They chose the 98% confidence and assumed that the population standard deviation was the same as in 2015 (68.75). Assume again that those salaries were normally distributed.

If they would like the (margin of) error to be no more than €60, how large a sample would they need to select?

Answer 1

Solution :

Given that,

standard deviation =   =68.75

Margin of error = E = 60

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

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

n = ( 2.326*68.75 /60 )2

n =7

Sample size = n =7