A Hypothesis Test for Two Population Standard Deviations Is to Be

question 17

Multiple Choice

A hypothesis test for two population standard deviations is to be performed. Independent random samples of sizes $\mathrm { n } _ { 1 }$ and $\mathrm { n } _ { 2 }$ are drawn from the two populations. The variable under consideration is normally distributed on each of the two populations. The test statistic is $\mathrm { s } _ { 1 } ^ { 2 } / \mathrm { s } _ { 2 } ^ { 2 }$ . If the null hypothesis, $\mathrm { H } _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 }$ , is true, what is the distribution of this test statistic?

• A)\(\chi ^ { 2 }\)-distribution with \(\mathrm { df } = \mathrm { n } _ { 1 } + \mathrm { n } _ { 2 } - 1\)
• B) \(\mathrm { F }\)-distribution with df \(= \left( \mathrm { n } _ { 1 } , \mathrm { n } _ { 2 } \right)\)
• C) F-distribution with \(\mathrm { df } = \left( \mathrm { n } _ { 2 } - 1 , \mathrm { n } _ { 1 } - 1 \right)\)
• D) \(F\)-distribution with \(\mathrm { df } = \left( \mathrm { n } _ { 1 } - 1 , \mathrm { n } _ { 2 } - 1 \right)\)

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Definitions:

Excess Capacity

This term refers to a situation where a firm produces at a lower scale than its potential, indicating that there are unused resources or the firm is operating below its efficient scale.

Profit-Maximizing Level

The point of operation where a firm achieves its highest profit, determined by the intersection of marginal cost and marginal revenue.

Marginal Cost

The cost escalation associated with the production of one more unit of a product or service.

Economic Loss

Occurs when total cost exceeds total revenue, not covering all explicit and implicit costs.