Suppose that \[55\%\] of the approximately \[4{,}000\] school-aged children in the county have vitamin deficiency. A nutritionist takes a cluster random sample of \[100\] of those children. They test the children for vitamin deficiency. They provide the children with vitamin-rich snacks at school for three months, then retest them. They plan to look at the difference \[(\text{after} - \text{before})\] between the proportions of children with vitamin deficiency.
Consider the formula:
\[\sigma_{\hat{p}_\text{A}-\hat{p}_\text{B}}=\sqrt{\dfrac{p_\text{A}\left(1-p_\text{A}\right)}{n_\text{A}}+\dfrac{p_\text{B}\left(1-p_\text{B}\right)}{n_\text{B}}}\]
Why is it not appropriate for the nutritionist to use this formula for the standard deviation of \[\hat{p}_\text{A}-\hat{p}_\text{B}\]?
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 for the students sampled before receiving the snacks.
B
We cannot assume independence for the students sampled before receiving the snacks.
(Choice C)
We cannot assume independence for the students sampled after receiving the snacks.
C
We cannot assume independence for the students sampled after receiving the snacks.