Please helpp!! Probability estimation!! : (

#1
City A has a population of 4 million, and city B has 6 million. Both cities have the same proportion of women. A random sample (with replacement) will be taken from each city to estimate this proportion . In each of the following cases, say whether the two samples give equally good estimates; and if you think one estimate is better than the other, say how much better it is.
a) a 0.01% sample from each city
b) a sample of size 400 from each city
c) a 0.1% sample from city A, and 0.075%sample from city B

PLEASE EXPLAIN THIS TO ME... SO FREAKING LOST. :'(
 

BGM

TS Contributor
#2
Under the assumption/hypoethesis that both city has the equal proportion, the estimator of the proportion will be the pooled sample mean from both city. So you just compare the total sample size in each case.

To quantify how much better, you may compare the sample size as above, or compare the standard error of your estimator for a given proportion.