A Researcher Wishes to Determine Whether the Blood Pressure of Vegetarians

A researcher wishes to determine whether the blood pressure of vegetarians is, on average, lower than the
blood pressure of nonvegetarians. Independent simple random samples of 85 vegetarians and 75
nonvegetarians yielded the following sample statistics for systolic blood pressure: $$\begin{array} { | l | l | } \hline { \text { Vegetarians } } & { \text { Nonvegetarians } } \\\hline n _ { 1 } = 85 & n _ { 2 } = 75 \\\hline \bar { x } _ { 1 } = 124.1 \mathrm { mmHg } & \bar { x } _ { 2 } = 138.7 \mathrm { mmHg } \\\hline s _ { 1 } = 38.7 \mathrm { mmHg } & s _ { 2 } = 39.2 \mathrm { mmHg } \\\hline\end{array}$$ Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of vegetarians is lower than the
mean systolic blood pressure of nonvegetarians. Include your null and alternative hypotheses, the test statistic, P-value
or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.