Question

The Roper poll states that 56% of the 1,021 Americans questioned think that UFOs are real. For each of the following levels of confidence, find the margin of error associated with the sample. (Round your answers to one decimal place.)

(a) an 80% level of confidence
± 2%

(b) a 90% level of confidence

Answer 1

Given that, n=1021
p^= 56% = 0.56
a) (1–α)%=80%
(1–α)=0.80
α=0.2
α/2=0.1

Zα/2=0.84 ....... from standard normal table.
Margin of error=E=Zα/2 ×√{[p^(1-p^)]/n}
=0.84 ×√{[0.56(1-0.56)]/1021}
=0.84 × 0.0155
= 0.0130

Margin of error=E=1.3% ... upto 1 decimal place.

b) (1–α)%=90%
(1–α)=0.90
α=0.1
α/2=0.05
Zα/2=1.645 ....... from standard normal table.
Margin of error=E=Zα/2 ×√{[p^(1-p^)]/n}
=1.645 ×√{[0.56(1-0.56)]/1021}
=1.645 × 0.0155
= 0.0255

Margin of error=E=2.5% ....upto 1 decimal place.