Maria is a college professor, and she wonders how the scores compare on her midterm and her final. She teaches two sections of a course, and each section has \[180\] students. She decides to take a random sample of \[10\] students from each section. For those students, she'll calculate the mean midterm score and the mean final score. She plans to look at the difference \[(\text{Final}-\text{Midterm})\] between those means.
Consider the formula:
\[\sigma_{\bar{x}_1-\bar{x}_2}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_\text{2}^2}{n_2}}\]
Why is it not appropriate to use this formula for the standard deviation of \[\bar{x}_\text{F}-\bar{x}_\text{M}\]?
Choose 1 answer:
Choose 1 answer:
(Choice A)
The samples are not independent of each other.
A
The samples are not independent of each other.
(Choice B)
We cannot assume independence between the midterm scores in the sample.
B
We cannot assume independence between the midterm scores in the sample.
(Choice C)
We cannot assume independence between the final exam scores in the sample.
C
We cannot assume independence between the final exam scores in the sample.