Question

You plan to construct a 99% confidence interval for the mean  of a normal population with (known) standard deviation . By using a sample size of 100 rather than 400, you can change the margin of error by a factor of? Justify.

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Answer 1

Formula for ME =

When sample size is 400 then:

When sample size is 100 then:

(because z and standard deviation are constant)

When we compare both margin of errors we see that ME got doubled in case of sample size 100 comparison to sample size of 400.

Hence, we can change the margin of error by a factor of 2.  

I hope this will help. Thank you.