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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 $29$ people who drank ethanol and another group of $29$ people given a placebo. The errors for the treatment group have a standard deviation of $2$.$10$ , and the errors for the placebo group have a standard deviation of $0$.$82$ . 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 th errors.$\newline$Let sample $1$ be the sample with the larger sample variance, and let sample $2$ be the sample with the smalle sample variance. What are the null and alternative hypotheses?$\newline$A. $H_{0}: \sigma_{1}^{2} \neq \sigma_{2}^{2}$$\newline$B. $H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2}$$\newline$$$\mathrm{H}_{1}: \sigma_{1}^{2}=\sigma_{2}^{2} \quad \mathrm{H}_{1}: \sigma_{1}^{2}>\sigma_{2}^{2}$$$\newline$C. $H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2}$$\newline$D.$\newline$$$\begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \end{array}$$$\newline$$$\mathrm{H}_{1}: \sigma_{1}^{2}<\sigma_{2}^{2}$$$\newline$Identify the test statistic.$\newline$$\square$ (Round to two decimal places as needed.)