Certainly! Let's solve the problem step-by-step.
1. Given information:
- Sample size ([tex]\( n \)[/tex]) = 144
- Standard deviation ([tex]\( \sigma \)[/tex]) = 1.5
2. Objective:
- To find the standard error (SE) rounded to three decimal places.
3. Formula for Standard Error:
[tex]\[
SE = \frac{\sigma}{\sqrt{n}}
\][/tex]
4. Calculation:
- First, calculate the square root of the sample size ([tex]\( n \)[/tex]):
[tex]\[
\sqrt{n} = \sqrt{144} = 12
\][/tex]
- Next, divide the standard deviation ([tex]\( \sigma \)[/tex]) by the square root of the sample size ([tex]\( \sqrt{n} \)[/tex]):
[tex]\[
SE = \frac{\sigma}{\sqrt{n}} = \frac{1.5}{12} = 0.125
\][/tex]
5. Result:
The standard error is:
[tex]\[
SE = 0.125
\][/tex]
So, the standard error to three decimal places is [tex]\( 0.125 \)[/tex].
