Question\text{Listed in the accompanying table are weights (lb) of samples of the contents of cans of regular Coke and Diet Coke. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) to (c).} \\
\text{a. Use a 0.01 significance level to test the claim that the contents of cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.} \\
\text{What are the null and alternative hypotheses? Assume that population 1 consists of regular Coke and population 2 consists of Diet Coke.} \\
\begin{itemize} \item \text{A. } H_{0}: \mu_{1} \leq \mu_{2} \quad H_{1}: \mu_{1}>\mu_{2} \item \text{B. } H_{0}: \mu_{1} \neq \mu_{2} \quad H_{1}: \mu_{1}>\mu_{2} \item \text{C. } H_{0}: \mu_{1}=\mu_{2} \item \text{D. } H_{0}: \mu_{1}=\mu_{2} \quad H_{1}: \mu_{1}>\mu_{2} \end{itemize}
\text{The test statistic is } \square \text{ (Round to two decimal places as needed.)} \\
\text{The P-value is } \square \text{ (Round to three decimal places as needed.)} \\
\text{State the conclusion for the test.} \\
\begin{itemize} \item \text{A. Reject the null hypothesis. There is not sufficient evidence to support the claim that cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.} \item \text{B. Reject the null hypothesis. There is sufficient evidence to support the claim that cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.} \item \text{C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that cans of regular Coke have weights with a mean that is greater than the mean for Diet Coke.} \item \text{D. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that cans of regular Coke have weights with a mean that} \end{itemize}
\begin{tabular}{|c|c|c|} \hline & \text{Regular Coke} & \text{Diet Coke} \\ \hline 1 & 0.81922 & 0.77732 \\ \hline 2 & 0.81502 & 0.77583 \\ \hline 3 & 0.81528 & 0.78963 \\ \hline 4 & 0.8211 & 0.78681 \\ \hline 5 & 0.8181 & 0.78436 \\ \hline 6 & 0.82472 & 0.7861 \\ \hline 7 & 0.80618 & 0.78062 \\ \hline 8 & 0.81235 & 0.78302 \\ \hline 9 & 0.81715 & 0.78319 \\ \hline 10 & 0.80936 & 0.7863 \\ \hline 11 & 0.83103 & 0.78013 \\ \hline 12 & 0.83103 & \\ \hline \end{tabular}