Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 22 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a standard deviation of 2.40 , and the errors for the placebo group have a standard deviation of 0.87 . Assume that the two populations are normally distributed. Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors.

Let sample 1 be the sample with the larger sample variance, and let sample 2 be the sample with the smaller sample variance. What are the null and alternative hypotheses?
A. $H_0:{\sigma }_1^2={\sigma }_2^2$
B.
$$H_1:{\sigma }_1^2<{\sigma }_2^2$$
$$\begin{array}{l}{H}_0:{\sigma }_1^2={\sigma }_2^2\\ H_1:{\sigma }_1^2\ne {\sigma }_2^2\end{array}$$
$$\text{ C. }\begin{array}{rl}{H}_0:{\sigma }_1^2& ={\sigma }_2^2\\ H_1:{\sigma }_1^2& >{\sigma }_2^2\end{array}$$
D.
$$\begin{array}{l}{H}_0:{\sigma }_1^2\ne {\sigma }_2^2\\ H_1:{\sigma }_1^2={\sigma }_2^2\end{array}$$

Identify the test statistic.
7.61 (Round to two decimal places as needed.)

Use technology to identify the P-value.
(Round to three decimal places as needed.)