Question

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? . The margin of error is multiplied by . The margin of error is multiplied by . The margin of error is multiplied by 0.5. The margin of error is multiplied by 2.

Answer 1

Answer:

The margin of error is multiplied by $\sqrt{2}$

Step-by-step explanation:

margin of error (ME) from the mean can be calculated using the formula

ME=$\frac{z*s}{\sqrt{N} }$ where

• z is the corresponding statistic of the given confidence level

• s is the standard deviation of the sample (or of the population if it is known)

• N is the sample size

Since margin of error is proportional with inverse of $\sqrt{N}$,

if we cut the sample size in half, the margin of error is multiplied by $\sqrt{2}$.