Question

17. A TV news magazine states that the results of their study of the average number of complaints per week

about garbage pick-up in the city had a margin of error of ±2.1 at the 95% confidence level, based on n = 30

weeks. For this statement to be true, what was the approximate population standard deviation that the

organization must have used to compute the margin of error?

Answer 1

17)

Solution :

Given that,

standard deviation = = ?

margin of error = E = 2.1

n = 30

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Population standard deviation = = (n² * E) / Z_/2

= ((30 * 2.1) / 1.96)²

= 5.87

Population standard deviation = 5.87