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

question 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.

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Definitions:

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A condition resulting from inadequate levels of vitamin D in the body, which is essential for healthy bones, immune function, and reducing the risk of chronic diseases.

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The lack of essential nutrients in the diet, leading to health problems and diseases.

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Inflammation

A biological response of body tissues to harmful stimuli, such as pathogens, damaged cells, or irritants, characterized by redness, swelling, heat, and pain.