A researcher wants to estimate the proportion of a population which possesses a given characteristic. A...
A researcher wants to estimate the proportion of a population which possesses a given characteristic. A random sample of size 200 is taken and 30% of the sample possesses the characteristic. The 90% confidence interval to estimate the population proportion is _______.
Homework Answers
p̂ = X / n = 60/200 = 0.3
p̂ ± Z(α/2) √( (p * q) / n)
0.3 ± Z(0.1/2) √( (0.3 * 0.7) / 200)
Z(α/2) = Z(0.1/2) = 1.645
Lower Limit = 0.3 - Z(0.1) √( (0.3 * 0.7) / 200) = 0.2467
upper Limit = 0.3 + Z(0.1) √( (0.3 * 0.7) / 200) = 0.3533
90% Confidence interval is ( 0.2467 , 0.3533
)
( 0.2467 < P < 0.3533 )
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