The standard deviation is 15. If a sample of 100 people is selected, compute the standard error of the mean. What size sample is necessary to double the standard error of the mean?

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Answer 1 · 2018-04-09T20:44:13

The standard error is 1.5.
The new sample size should be 25 (one-quarter of 100).

The formula for standard error #(SE)# of the mean is

#SE = sigma/sqrtn#

Knowing #sigma=15# and #n=100#, we compute:

#SE=15/sqrt(100)=15/10=1.5#

If we want to double the standard error #SE# by changing the sample size #n#, we need a sample that is #1/4# as large—that is, 25. This is because:

#SE=15/sqrt(25)=15/5=3#

And 3 is twice as much as 1.5.

Mathematically:

We want #SE_"new"=2SE# by using a new #n#.

#=> cancelsigma/sqrt(n_"new")=2cancelsigma/sqrtn#

#=> sqrt(n_"new")=sqrtn/2#

#=> n_"new"=n/4#