Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

question 89

Multiple Choice

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-Ten different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. Construct a $90 \%$ confidence interval for the mean of the differences.
$\begin{array}{lllllllllll}\text { Before } & 33 & 33 & 38 & 33 & 35 & 35 & 40 & 40 & 40 & 31 \\\hline \text { After } & 34 & 28 & 25 & 28 & 35 & 33 & 31 & 28 & 35 & 33\end{array}$

• A) \(1.5 < \mu _ { \mathrm { d } } < 8.1\)
• B) \(3.8 < \mu _ { \mathrm { d } } < 5.8\)
• C) \(1.8 < \mu _ { \mathrm { d } } < 7.8\)
• D) \(2.5 < \mu _ { \mathrm { d } } < 7.1\)

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Definitions:

Testable Hypothesis

A hypothesis that can be supported or refuted through experimentation or observation.

Scientific Investigation

A systematic process for acquiring new knowledge about the natural world based on observable, empirical evidence.

Analyse

To examine something in detail in order to understand it better or discover more about it.

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The process of formally presenting results or discoveries from research, investigations, or assessments to a relevant audience.