Test Hypotheses Regarding Two Population Standard Deviations
-Test the Hypothesis $\sigma _ { 1 } > \sigma _ { 2 }$

question 78

Multiple Choice

Test Hypotheses Regarding Two Population Standard Deviations
-Test the hypothesis that $\sigma _ { 1 } > \sigma _ { 2 }$ at the $\alpha = 0.01$ level of significance for the given sample data.
$\begin{array}{c|cc} & \text { Population 1 } & \text { Population 2 } \\\hline \mathrm{n} & 61 & 31 \\\mathrm{~s} & 27.5 & 26.3\end{array}$

• A) Test statistic: \(\mathrm { F } = 1.09\). Critical value \(= 2.21\). Do not reject \(\mathrm { H } _ { 0 }\).
• B) Test statistic: \(\mathrm { F } = 1.09\). Critical value \(= 2.03\). Reject \(\mathrm { H } _ { 0 }\).
• C) Test statistic: \(\mathrm { F } = 28.75\). Critical value \(= 2.03\). Reject \(\mathrm { H } _ { 0 }\).
• D) Test statistic: \(\mathrm { F } = 1.05\). Critical value \(= 2.21\). Do not reject \(\mathrm { H } _ { 0 }\).

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Definitions:

Social Inequality

The presence of unequal opportunities and rewards for different social positions or statuses within a group or society.

Functional

Working or operating in a way that fulfills the purpose or task for which something was designed.

Upper Class

A social group at the top of a socioeconomic hierarchy, usually possessing significant wealth, power, and influence.

Capitalist Economy

An economic system in which private individuals rather than the state own and control property and businesses, and the production of goods and services is based on supply and demand in the market.