solution:
Given that, n=2973, X=1424
p^=X/n
= 1424/2973
= 0.479
The best point estimate of population proportion p is p^=
0.479
(1–α)%=99%
(1–α)=0.99
α=0.01
α/2=0.005
Zα/2=2.58 ....... from standard normal table.
Margin of error=E=Zα/2 ×√{[p^(1-p^)]/n}
=2.58 ×√{[0.479(1-0.479)]/2973}
=1.96 × 0.0092
= 0.0237
Margin of error=E=0.0237
99% Confidence Interval for true population proportion p is given
as,
p^ ± Margin of error
=(0.479-0.0237,0.479+0.0237)
=(0.4553,0.5027)
Lower limit =0.4553
Upper limit=0.5027
A 99% confidence interval for the population proportion is
(0.4553,0.5027)
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