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

question 148

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.
-The table below shows the weights of 9 subjects before and after following a particular diet for two months.
$\begin{array}{r|ccccccccc}\text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } \\\hline \text { Before } & 168 & 180 & 157 & 132 & 202 & 124 & 190 & 210 & 171 \\\hline \text { After } & 162 & 178 & 145 & 125 & 171 & 126 & 180 & 195 & 163\end{array}$

Construct a $99 \%$ confidence interval for the mean difference of the "before" minus "after" weights.

• A) \(2.8 < \mu _ { \mathrm { d } } < 17.0\)
• B) \(- 0.6 < \mu _ { \mathrm { d } } < 20.4\)
• C) \(2.4 < \mu _ { \mathrm { d } } < 17.4\)
• D) \(4.51 < \mu _ { \mathrm { d } } < 15.7\)

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Definitions:

Population Standard Deviation

Represents the degree to which individual data points in a full set deviate from the population mean, giving insight into the variability within the entire group.

Standard Deviation

A statistical measure that quantifies the amount of variation or dispersion of a set of data values, indicating how spread out the data points are from the mean.

Set of Data

A collection of numbers or values that are usually related and can be analyzed statistically.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values in a data set differ from the mean.