The manufacturer notices the production costs for ALLOY 2 + Treatment is the same as ALLOY 3. If he wants to produce just one of the two rods (ALLOY 2 + Treatment or ALLOY 3), which one should he pick? In this part, you will compare the mean strength of ALLOY 2 + TREATMENT rods and ALLOY 3 rods. Can we conclude that ALLOY 2 rods after the treatment are stronger than ALLOY 3 rods, on the average? Answer the question by carrying out the appropriate test in the Data Analysis menu. State the hypotheses tested and the distribution of the test statistic under the null hypothesis. Report the value of the test statistic provided by Excel, the p-value, and your conclusion.

\begin{tabular}{rrrr} ALLOY 1 & ALLOY 2 & ALLOY 3 & ALLOY 2 + TREATMENT \\ 63.7 & 64.7 & 65 & 66.5 \\ 64 & 63.6 & 64.5 & 66 \\ 66.4 & 66.5 & 64.8 & 67.3 \\ 64.8 & 65 & 65.3 & 66.8 \\ 63.2 & 64.6 & 68.2 & 66.5 \\ 63.8 & 64.8 & 63.8 & 66.1 \\ 64 & 66.3 & 66.8 & 66.9 \\ 65.6 & 65.1 & 64.8 & 66.3 \\ 63.9 & 64.2 & 64.2 & 66.9 \\ 64.3 & 64.5 & 63.2 & 67.1 \\ 65.7 & 65.9 & 66.8 & 66.7 \\ 63.8 & 64.3 & 64.7 & 66.2 \\ 68.5 & 67 & 66.7 & 68.2 \\ 68.3 & 66.2 & 66.9 & 67.1 \\ 66.8 & 65.3 & 66 & 66.9 \\ 65.4 & 65.1 & 65.4 & 66.9 \\ 65.8 & 65.2 & 64.2 & 66.3 \\ 63.1 & 64.1 & 65.4 & 66.9 \\ 68.9 & 66.5 & 65.3 & 67.3 \\ 64.5 & 65 & 66.8 & 66.6 \\ 62.3 & 64.5 & 65.3 & 66.8 \\ 64.7 & 65 & 65 & 66.5 \\ 66.8 & 65.3 & 64.1 & 66.6 \\ 67.4 & 67.8 & 66.6 & 68.1 \\ 63.8 & 63.5 & 65.2 & 66.7 \\ 65.2 & 65.1 & 65.4 & 66.9 \\ 63.6 & 64.2 & 64.1 & 66.7 \\ 67.7 & 66.1 & 65.4 & 66.9 \\ 64.1 & 64.4 & 65 & 66.5 \\ 63 & 64.7 & 65.1 & 66.6 \end{tabular} \begin{tabular}{rrrr} ALLOY 1 & ALLOY 2 & ALLOY 3 & ALLOY 2 + TREATMENT \\ 63.7 & 64.7 & 65 & 66.5 \\ 64 & 63.6 & 64.5 & 66 \\ 66.4 & 66.5 & 64.8 & 67.3 \\ 64.8 & 65 & 65.3 & 66.8 \\ 63.2 & 64.6 & 68.2 & 66.5 \\ 63.8 & 64.8 & 63.8 & 66.1 \\ 64 & 66.3 & 66.8 & 66.9 \\ 65.6 & 65.1 & 64.8 & 66.3 \\ 63.9 & 64.2 & 64.2 & 66.9 \\ 64.3 & 64.5 & 63.2 & 67.1 \\ 65.7 & 65.9 & 66.8 & 66.7 \\ 63.8 & 64.3 & 64.7 & 66.2 \\ 68.5 & 67 & 66.7 & 68.2 \\ 68.3 & 66.2 & 66.9 & 67.1 \\ 66.8 & 65.3 & 66 & 66.9 \\ 65.4 & 65.1 & 65.4 & 66.9 \\ 65.8 & 65.2 & 64.2 & 66.3 \\ 63.1 & 64.1 & 65.4 & 66.9 \\ 68.9 & 66.5 & 65.3 & 67.3 \\ 64.5 & 65 & 66.8 & 66.6 \\ 62.3 & 64.5 & 65.3 & 66.8 \\ 64.7 & 65 & 65 & 66.5 \\ 66.8 & 65.3 & 64.1 & 66.6 \\ 67.4 & 67.8 & 66.6 & 68.1 \\ 63.8 & 63.5 & 65.2 & 66.7 \\ 65.2 & 65.1 & 65.4 & 66.9 \\ 63.6 & 64.2 & 64.1 & 66.7 \\ 67.7 & 66.1 & 65.4 & 66.9 \\ 64.1 & 64.4 & 65 & 66.5 \\ 63 & 64.7 & 65.1 & 66.6 \end{tabular}