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:

Framing Effects

Cognitive biases where people's decisions are influenced by the way information is presented, rather than just the information itself.

Anchoring

Anchoring is a psychological phenomenon wherein an individual relies too heavily on an initial piece of information, or 'anchor,' to make subsequent decisions.

Heuristics

Simple, efficient rules, either hard-coded by evolutionary processes or learned, which help in making decisions, forming judgments, or solving problems.

Error-Free Decisions

Decisions made without mistakes, achieved through careful analysis, planning, and consideration of all relevant information.