A recent Gallop poll showed that 672 of 1019 adults nationwide think that marijuana should be legalized
Find the margin of error that corresponds to a 95% confidence interval.
Homework Answers
Part a)
Margin of Error = Z(α/2) √ ( (p*q) / n) = 0.0291
Part b)
p̂ = X / n = 672/1019 = 0.6595
p̂ ± Z(α/2) √( (p * q) / n)
0.6595 ± Z(0.05/2) √( (0.6595 * 0.3405) / 1019)
Critical value Z(α/2) = Z(0.05/2) = 1.96 ( From Z table
)
Lower Limit = 0.6595 - Z(0.05) √( (0.6595 * 0.3405) / 1019) =
0.6304
upper Limit = 0.6595 + Z(0.05) √( (0.6595 * 0.3405) / 1019) =
0.6886
95% Confidence interval is ( 0.6304 , 0.6886 )
( 0.6304 < P < 0.6886 )
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