At the 0.05 significance level,
the lower limit of confidence interval is approx. 0.018 and upper limit of confidence interval is approx.0.182...
A relief fund is set up to collect donations.
first Sample size, n₁ = 200
Second sample, n₂ = 200
28% of those 200 people's who contacted by telephone , p₁-cap = 28% = 0.28
18% of the 200 who received mail requests, p₂-cap = 0.18
significance level, α = 0.05
S.E for difference between proportions
= √(p₁-cap(1-(p₁-cap))/n₁ + p₂-cap(1-(p₂-cap))/n₂)
= √0.28(1-0.28)/200 + 0.18(1-0.18)/200
= √0.28(0.72)/200 + 0.18(0.82)/200
= 0.04178 ~ 0.0418
the z-value for significance level 0.05, Zα/2 = Z₀.₀₂₅ = 1.96 (from Z-table)
Margin of error = α/2 ( S.Eₚ₁ ₋ₚ₂)
= 1.96× 0.0418 = 0.08189
CI is given by (p₁-cap - p₂-cap) +- Zα/2 ( S.E )
Lower limit = (0.28-0.18)+ 0.08189
=0.01818 ~ 0.018
Upper limit = (0.28-0.18) - 0.08189
= 0.18189~0.182
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