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:

Residual Income

The income that remains after deducting all required costs of capital from the operating income.

Imputed Interest

The interest that is considered or assumed to be charged on an interest-free loan or bond, often for tax calculations.

Residual Income

The income that remains after subtracting all the costs of capital from the net operating income.

Net Operating Income

Earnings before interest and taxes (EBIT), a measure of a company's profitability from operations.