Question

I have a question about the rejection region in this problem (attached as comment)

Answer 1

So i don't quite understand what the rejection region actually involves in this question

Answer 2

I understand the layout, for the rejection region of the lower tail area, it would be some interval that includes Zero up to the upper bound of the two-sided interval.
Alternatively the upper tail area would include the lower bound of the two-sided interval up to infinity.
I just fail to understand how to conclude what results would be considered accepted Vs. rejected.

Answer 3

I came up with the following, and would like to know if it's correct
For an Upper tail area Rejection Region\[RR=\left\{ S_{x}^{2},S _{y}^{2}:\frac{ S_{x}^{2} }{ S_{y}^{2} }>1 \right\}\]For a Lower tail area Rejection Region\[RR=\left\{ S_{x}^{2},S _{y}^{2}:\frac{ S_{x}^{2} }{ S_{y}^{2} }<1 \right\}\]and as for the two-tailed region, it would just be the union of those two\[RR=\left\{ S_{x}^{2},S _{y}^{2}:(\frac{ S_{x}^{2} }{ S_{y}^{2} }<1) \cup (\frac{ S_{x}^{2} }{ S_{y}^{2} }>1)\right\}\]any confirmation on anything i've said would be very much appreciated :)

Answer 4

Actually i'm starting to think that the Two-tailed region should be more like this\[RR=\left\{S _{x}^{2},S _{y}^{2}: A<\frac{ S_{x}^{2} }{ S_{y}^{2} }<B \right\}\]Or some kind of interval that that incorporates the actual difference in the variances of the two companies (which would be the best interval for the Dairy manager to use)
Slowly answering my own question.