A Researcher Wishes to Determine Whether the Blood Pressure of Vegetarians

question 65

Essay

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.

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Definitions:

Marginal Means

The average value of a variable across different levels of another variable, commonly used in the analysis of variance.

Significant Main Effect

In statistical analysis, a main effect that has been tested and found to statistically differ significantly from what would be expected by chance.

Crime Area

A geographical region or locale known to have a high incidence of criminal activity.

Marginal Mean

The average value of a variable across different levels of another variable, typically used in the context of analysis of variance.