Let

X _ { 1 } , \ldots \ldots , X _ { 20 }

be a random sample from a normal distribution with variance

\sigma _ { 1 } ^ { 2 } , \mathrm { let } Y _ { 1 } , \ldots \ldots , Y _ { 25 }

be another random sample (independent of the

\left. X _ { 2 } ^ { \prime } s \right)

from a normal distribution with variance

\sigma _ { 1 } ^ { 2 } , \text { and let } S _ { 1 } ^ { 2 } \text { and } S _ { 1 } ^ { 2 }

denote the two sample variances. Which of the following statements are not true in testing

H _ { 0 } : σ _ { 1 } ^ { 2 } = σ _ { 2 } ^ { 2 } ,

where the test statistic value is

f = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }

and the test is performed at .10 level?
A) The rejection region is

f \geq F _ { 10,19,24 } \text { if } H _ { 0 } : \sigma _ { 1 } ^ { 2 } > \sigma _ { 2 } ^ { 2 }

B) The rejection region is

f \leq F _ { 90,19,24 } \text { if } H _ { 0} : \sigma _ { 1 } ^ { 2 } < \sigma _ { 2 } ^ { 2 }

C) The rejection region is either

f \geq F _ { 10,19,24 } \text { or } \mathrm { f } \leq \mathrm { F } _ { 90,19,24 }

D) All of the above statements are true.
E) None of the above statements are true.

Provided That at Least One of the Sample Sizes M μ1−μ2,\mu _ { 1 } - \mu _ { 2} ,μ1​−μ2​,

Essay