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

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. $$\begin{array} { l } \text {Treatment Group}\\\mathrm { n } _ { 1 } = 100 \\\overline { \mathrm { x } } 1 = 178 \\\sigma _ { 1 } = 35\end{array}$$ $$\begin{array} { l } \text {Control Group}\\\mathrm { n } _ { 2 } = 100 \\\overline { x _ { 2 } } = 193 \\\sigma _ { 2 } = 37\end{array}$$