Question

All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sam

to make a statistical inference about the mean of the normally distributed population from which it was drawn?
ME-
Z.S
O The margin of error is multiplied by √0.5.
O The margin of error is multiplied by √√2-
O The margin of error is multiplied by 0.5.
O The margin of error is multiplied by 2.

Answer 1

When you cut the sample size in half while making a statistical inference about the mean of a normally distributed population, the effect on the margin of error depends on the relationship between the sample size and the margin of error. Generally, the margin of error is inversely proportional to the square root of the sample size.

So, if you reduce the sample size by half, it means you are taking a smaller sample, which will result in a larger margin of error. In other words, the margin of error is multiplied by a factor greater than 1.

Among the given options, the correct answer is:

D. The margin of error is multiplied by 2.

This option correctly reflects the relationship between reducing the sample size by half and the resulting increase in the margin of error.