We want to estimate π using a confidence interval that has a 3% margin of error, and we want to have 99% confidence that our interval captures π. We think that π is between .4 and .6. What sample size should we use?
Margin of error = (0.6 - 0.4)/2 = 0.1
+ E = 0.6
Or,
+ 0.1 = 0.6
Or,
= 0.5
At 99% confidence level, the critical value is z0.005 = 2.575
Margin of error = 0.03
Or, z0.005 * sqrt((1
-
)/n) = 0.03
Or, 2.575 * sqrt(0.5(1 - 0.5)/n) = 0.03
Or, n = (2.575 * sqrt(0.5 * 0.5)/0.03)^2
Or, n = 1842
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