Question

A 2005 poll reported that 78​% of people worried that they would be exposed to SARS. Find the approximate margin of error if ​(a) nequals119​, ​(b) nequals314​, ​(c) nequals1993. Explain how the margin of error changes as n increases.

Answer 1

(a) Margin of error = 0.038

(b) Margin of error = 0.023

(c) Margin of error = 0.0093

The margin of error decreases as n increases

Step-by-step explanation:

Margin of error (E) = sqrt[p(1-p) ÷ n]

p is the population proportion = 0.78

n is sample size

(a) n = 119

E = sqrt[0.78(1 - 0.78) ÷ 119] = sqrt[1.442×10^-3] = 0.038

(b) n = 314

E = sqrt[0.78(1 - 0.78) ÷ 314] = sqrt[5.465×10^-4] = 0.024

(c) n = 1993

E = sqrt[0.78(1 - 0.78) ÷ 1993] = sqrt[8.610×10^-5] = 0.0093

The margin error decreases as n increases because the relationship between E and n is inverse in which an increase in one quantity (n) leads to a corresponding decrease in other quantity (E)