00:02
A 95 % confidence interval with margin of error plus or minus 0 .5 is built from a sample with data containing sample size n equals 50.
00:13
We want to answer to achieve a margin of error plus or minus 0 .25, what must the sample size n be? so, critically, let's remember an important definition.
00:26
The margin of error is equal to the critical t value times standard deviation s over root n.
00:32
So, if we assume that the critical value t and the standard deviation s cannot be changed, there's nothing in this question to suggest that we can alter these values.
00:41
It must be that we can use our n value to drive our new e value.
00:46
So let e1 equal 0 .5, our original e2 equal 0 .25 for the new e we want to obtain, and n1 is equal to 50.
00:55
If we write the ratio of these two values, e2 over e1, because we just address that t and s do not change, e2 over e1 simplifies to root n1 over root n2.
01:09
So we see that we can use e2, e1, and n1 to find the n2 or the sample size necessary to achieve our margin of error...