Perform the Indicated Hypothesis Test Use a Significance Level of 0

Essay

Perform the indicated hypothesis test. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (?1 = ?2), so that the standard error of the difference between means is obtained by pooling the sample variances .
-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:
$$\begin{array} { l l } \text { Vegetarians } & \text { Nonvegetarians } \\\hline \mathrm { n } _ { 1 } = 85 & \mathrm { n } _ { 2 }= 75 \\\overline { \mathrm { x } _ { 1 } } = 124.1 \mathrm { mmHg } & \overline { \mathrm { x }} _ { 2 } = 138.7 \mathrm { mmHg } \\\mathrm { s } _ { 1 } = 38.7 \mathrm { mmHg } & \mathrm { s } _ { 2 } = 39.2 \mathrm { mmHg }\end{array}$$
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 method of hypothesis testing.