A Researcher Wishes to Determine Whether People with High Blood $\mu _ { 1 } - \mu _ { 2 } .$

question 21

Essay

A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by
following a certain diet. A treatment group and a control group are selected. Assume the two samples are
random and independent. Construct a 90% confidence interval for the difference between the two population
means, $\mu _ { 1 } - \mu _ { 2 } .$ Would you recommend using this diet plan? Explain your reasoning. $$\begin{array} { l } \text {Treatment Group}\\\mathrm { n } _ { 1 } = 100 \\\overline { \mathrm { x } } 1 = 178 \\\sigma _ { 1 } = 35\end{array}$$ $$\begin{array} { l } \text {Control Group}\\\mathrm { n } _ { 2 } = 100 \\\overline { x _ { 2 } } = 193 \\\sigma _ { 2 } = 37\end{array}$$

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Definitions:

Legacy-creating Stage

A phase in life where individuals focus on what they will leave behind for future generations, often concerning their impact and contributions to society.

Post-formal Thought

A stage of cognitive development posited to follow Piaget’s final stage, characterized by the ability to understand that answers to problems can vary depending on circumstances and that ambiguity and contradiction are a part of life.

Practical

Related to the actual experience or use of knowledge in real-world situations, emphasizing effective action or application rather than theory.

Abstractly

Thinking in a way that is not concrete or specific, involving concepts and ideas rather than physical examples.