A Hypothesis Test for Two Population Standard Deviations Is to Be

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 hypotheses are:
$\begin{array} { r } \mathrm { H } _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 } \\\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } < \sigma _ { 2 }\end{array}$
Which of the following would provide evidence against the null hypothesis in favor of the alternative?

A) $\mathrm { s } _ { 1 } ^ { 2 } / \mathrm { s } _ { 2 } ^ { 2 }$ is too close to 1 .
B) $\mathrm { s } _ { 1 } ^ { 2 } / \mathrm { s } _ { 2 } ^ { 2 }$ is much bigger or much smaller than 1 .
C) $\mathrm { s } _ { 1 } ^ { 2 } / \mathrm { s } _ { 2 } ^ { 2 }$ is much bigger than 1 .
D) $\mathrm { s } _ { 1 } ^ { 2 } / \mathrm { s } _ { 2 } ^ { 2 }$ is much smaller than 1 .