SOLUTION: In a random sample of 200 observations,we found the proportion of successes to be 48%. A)Use a 90% degree of confidence to estimate the population proportion of successes of N=500

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Question 1121006: In a random sample of 200 observations,we found the proportion of successes to be 48%.
A)Use a 90% degree of confidence to estimate the population proportion of successes of N=500 and n = 1000 and comment on the difference in answers of A and B
Answer by Boreal(15235) About Me  (Show Source):
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The half interval for 90% CI is +/- z*SE, where z is 1.645 and SE is sqrt(.48*.52/n)
For n=500 the SE is 0.0223 and the half interval 0.0368
(0.4432, 0.5168)
Fon n=1000, the SE is 0.0158 and the half interval 0.026
(0.454, 0.506)
As the sample size increases, the SE decreases meaning that the estimate of the true number has less uncertainty the larger the sample. As the sample approaches the population size, the uncertainty approaches 0. That would occur only at extremely large sample sizes (it would be +/-0.001 for a sample size of a million).