Preliminary Data Analyses Indicate That You Can Reasonably Use Nonpooled $\begin{array}{l} \text { Vegetarians } \\\hline \mathrm{n}_{1}=85 \\\overline{\mathrm{x}_{1}}=124.1 \\\mathrm{~s}_{1}=38.7\end{array}$

Preliminary data analyses indicate that you can reasonably use nonpooled t-procedures on the given data. Apply anonpooled t-test to perform the required hypothesis test, using either the critical-value approach or the P-value approachas indicated.
-A researcher wishes to determine whether the systolic blood pressure of people who follow a vegetarian diet is, on average, lower than the systolic blood pressure of those who do not follow a vegetarian diet. Independent simple random samples of 85 vegetarians and 75 nonvegetarians yielded the following sample statistics: $\begin{array}{l} \text { Vegetarians } \\\hline \mathrm{n}_{1}=85 \\\overline{\mathrm{x}_{1}}=124.1 \\\mathrm{~s}_{1}=38.7\end{array}$

$\begin{array}{l} \text { Nonvegetarians } \\\hline \mathrm{n}_{2}=75 \\\overline{\mathrm{x}_{2}}=138.7 \\\mathrm{~s}_{2}=39.2\end{array}$
Use a significance level of 0.01 to test the claim that the mean systolic blood pressure for vegetarians is lower than the mean systolic blood pressure for nonvegetarians. Use the P-value approach.