Construct and Interpret Confidence Intervals Regarding the Difference of Two $90 \%$

question 62

Short Answer

Construct and Interpret Confidence Intervals Regarding the Difference of Two Independent Means
-A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by performing yoga exercises. A treatment group and a control group are selected. The sample statistics are given below. Construct a $90 \%$ confidence interval for the difference between the two population means, $\mu _ { 1 } - \mu _ { 2 }$ .
Would you recommend using yoga exercises? Explain your reasoning.
Treatment Group Control Group
$$\begin{array} { l l } \mathrm { n } 1 = 100 & \mathrm { n } _ { 2 } = 100 \\\overline { \mathrm { x } } 1 = 178 & \overline { \mathrm { x } } 2 = 193 \\\mathrm {~s} _ { 1 } = 35 & \mathrm {~s} _ { 2 } = 37\end{array}$$

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Definitions:

Division of Labor

This term refers to the assignment of different parts of a manufacturing process or task to different people in order to improve efficiency.

Cultural Diffusion

The process through which cultural elements, such as beliefs, technologies, and customs, spread from one society or cultural group to another.

Repressive State Control

Methods used by a government to control its citizens and maintain authority through restrictions and suppressing dissent.

Mobilized Opposition

Organized efforts to counter an initiative, policy, or legislation, often involving grassroots campaigning, protests, or lobbying.