SOLUTION: assume that a sample is drawn and z(a/2)= 1.96 AND 0=25. Answer the following questions: a) if the maximum error of estimate is 0.04 for this sample, what would be the sample size

Question 612660: assume that a sample is drawn and z(a/2)= 1.96 AND 0=25. Answer the following questions:
a) if the maximum error of estimate is 0.04 for this sample, what would be the sample size?
b) given that the sample size is 400 with this same z(a/2) and 0, what would be the Maixmum Error of estimate?
c) what happens to the maximum error of estimate as the sample size gets smaller?
d) what effect does the answer to C above have to the size of the confidence interval?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
assume that a sample is drawn and z(a/2)= 1.96 AND 0=25. Answer the following questions:
a) if the maximum error of estimate is 0.04 for this sample, what would be the sample size?
------
ME = z*s/sqrt(n)
0.04 = 1.96*25/sqrt(n)
sqrt(n) = 1.96*25/0.04 =
n = 35
====================================
b) given that the sample size is 400 with this same z(a/2) and s, what would be the Maxmum Error of estimate?
ME = 1.96*25/sqrt(400) = 2.45
====================================
c) what happens to the maximum error of estimate as the sample size gets smaller?
ME = z*s/sqrt(n)
Notice that ME and n are inversely related.
As n gets smaller, ME gets larger.
-----------------------------------------------
d) what effect does the answer to C above have to the size of the confidence interval?
The size of the CI is ALWAYS 2*ME
So, as n gets smaller, ME get larger, and CI get larger.
That means, as the sample size gets smaller the CI has to
be broader so we can have the same level of confidence that
it contains the population parameter we are interested in.
===========================
Cheers,
Stan H.

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