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

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) (Show Source): You can put this solution on YOUR website!
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).

RELATED QUESTIONS
Dear Tutor please help me with stats question In a random sample of 200... (answered by Theo)

In a random sample of 200 observations, we found the proportion of successes to be 48%... (answered by Boreal)

In a random sample of 200 observations, we found the proportion of successes to be 48 %. (answered by Boreal)

In a random sample of 500 observations, we found the proportion of success to be 48%.... (answered by AnlytcPhil)

In a random sample of 380 residents of Fiction County, it was found that only 57 could... (answered by Boreal)

In a sample of 200, we observe 140 successes. Is this sufficient evidence at the 1%... (answered by ewatrrr)

We use the t distribution to construct a confidence interval for the population mean when (answered by Theo)

in a random sample of 900 observations from a binomial population produced x = 378... (answered by stanbon)

A random sample of n = 900 observations from a binomial population produced x = 691... (answered by Theo)