Test the Indicated Claim About the Means of Two Populations

Test the indicated claim about the means of two populations. 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. A researcher wishes to determine whether people with high blood pressure can
reduce their blood pressure, measured in mm Hg, by following a particular diet. Use a significance level of 0.01
to test the claim that the treatment group is from a population with a smaller mean than the control group.
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. $$\begin{array} { | l | l | } \hline \hline { \text { Treatment Group } } & { \text { Control Group } } \\\hline n _ { 1 } = 35 & n _ { 2 } = 75 \\\hline \bar { x } _ { 1 } = 189.1 & \bar { x } _ { 2 } = 203.7 \\\hline s _ { 1 } = 38.7 & s _ { 2 } = 39.2 \\\hline \hline\end{array}$$