Independent Random Samples Selected from Two Normal Populations Produced the

question 39

Essay

Independent random samples selected from two normal populations produced the
following sample means and standard deviations. $\begin{array}{ll}\text { Sample 1 } & \text { Sample } 2 \\n_{1}=14 & n_{2}=11 \\\overline{x_{1}}=7.1 & \bar{x}_{2}=8.4 \\s_{1}=2.3 & s_{2}=2.9\end{array}$

Find and interpret the $95 \%$ confidence interval for $\left( \mu _ { 1 } - \mu _ { 2 } \right)$ .

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Definitions:

Systematic Errors

Suboptimal choices that (1) are not rational because they do not maximize a person’s chances of achieving his or her goals and (2) occur routinely, repeatedly, and predictably.

Self-Interested

Acting in a way that is most beneficial to oneself, often used in the context of economic behavior assuming individuals act to maximize their own welfare.

Willpower

The ability to resist short-term temptations in order to meet long-term goals.

Systematic Error

Errors in measurement that are consistent, predictable, and typically caused by faulty equipment or bias, which can lead to inaccuracies in data collection or analysis.