Question

A certain region would like to estimate the proportion of voters who intend to participate in upcoming elections. A pilot sample of 50 voters found that 32 of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a 97% interval with a margin of error equal to 0.08 to estimate the proportion. The region should sample additional voters. (Round up to the nearest integer.)

Answer 1

Let p̂ be the sample proportion of voters intending to vote                      
32 out of 50 intend to vote                      
p̂ = 32/50 = 0.64                      
                      
Confidence interval for population proportion is given by                      

p(1-0) +z* n

where n is the sample size                      
z is the z score                      
                      
Margin of Error = 0.08                      

P(1-P) Z* = 0.08 n

For 97%, α = 0.03, α/2 = 0.015                      
From the z-tables, or Excel function NORM.S.INV(α/2)                      
z = NORM.S.INV(0.015) = 2.17           (We take the positive value for calculations)          
To find 'n'                      

0.64(1 – 0.64) 2.17* = 0.08 n n = (2.17)2 0.64(1 – 0.64) (0.08)2

n = 169.52                      
n = 170   …Rounding up                  
                      
Additional voters to be sampled = 170 - 50 = 120                      
                      
The region should sample 120 additional voters                      

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