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?

(me = \frac{z cdot s}{sqrt{n}})

• the margin of error is multiplied by (sqrt{0.5}).
• the margin of error is multiplied by (sqrt{2}).
• the margin of error is multiplied by (0.5).
• the margin of error is multiplied by (2).

Explanation:

State the given formula and variables

Using the Margin of Error Calculation knowledge point

$$ ME = \frac{z \cdot s}{\sqrt{n}} $$

where \(ME\) is the margin of error, \(z\) is the critical value, \(s\) is the sample standard deviation, and \(n\) is the sample size.

Substitute the new sample size

Using the Margin of Error Calculation knowledge point

$$
LATEXBLOCK0
$$

Answer:

• The margin of error is multiplied by \(\sqrt{0.5}\).
• The margin of error is multiplied by \(\sqrt{2}\). (Correct answer)
• The margin of error is multiplied by 0.5.
• The margin of error is multiplied by 2.