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

Multiple Choice

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.