All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample
to make a statistical inference about the mean of the normally distributed population from which it was drawn?
zes
ME=
O The margin of error is multiplied by 0.5
O The margin of error is multiplied by a
O The margin of error is multiplied by 0.5.
O The margin of error is multiplied by 2.

Question

11-05-2021
Mathematics

contestada

All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample
to make a statistical inference about the mean of the normally distributed population from which it was drawn?
zes
ME=
O The margin of error is multiplied by 0.5
O The margin of error is multiplied by a
O The margin of error is multiplied by 0.5.
O The margin of error is multiplied by 2.

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joaobezerra joaobezerra · Answer 1 · 2021-05-16T02:08:24+02:00

Answer:

The margin of error is multiplied by 4.

Step-by-step explanation:

Margin of error is:

[tex]M = \frac{zs}{\sqrt{n}}[/tex]

In which z is related to the confidence level, s is elated to the standard deviation and n is the sample size.

From this, we have that the standard deviation is inversely proportional to the square root of the sample size.

If you cut the sample size in half:

The margin of error is inversely proportional to the square root of the sample size, so if you cut the sample size by [tex]\frac{1}{2}[/tex], the margin of error will be multiplied by [tex]2^2 = 4[/tex]

So

The margin of error is multiplied by 4.