Construct and Interpret Confidence Intervals about the Population Mean Difference of Matched -Pairs Data
-Construct a $99 \%$ confidence interval for data sets $\mathrm { A }$ and $\mathrm { B }$. Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent.
$\begin{array}{c|lllll}
\text { A } & 5.8 & 6.8 & 8.7 & 5.7 & 5.8 \
\hline \text { B } & 8.2 & 7.1 & 7.0 & 6.9 & 8.3
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $( - 4.502,2.622 )$
B) $( - 25.123,5.761 )$
C) $( - 21.342,18.982 )$
D) $( - 15.123,15.123 )$

Question

Construct and Interpret Confidence Intervals about the Population Mean Difference of Matched -Pairs Data
-Construct a $99 \%$ confidence interval for data sets $\mathrm { A }$ and $\mathrm { B }$. Data sets $\mathrm { A }$ and $\mathrm { B }$ are dependent.
$\begin{array}{c|lllll}
\text { A } & 5.8 & 6.8 & 8.7 & 5.7 & 5.8 \
\hline \text { B } & 8.2 & 7.1 & 7.0 & 6.9 & 8.3
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $( - 4.502,2.622 )$
B) $( - 25.123,5.761 )$
C) $( - 21.342,18.982 )$
D) $( - 15.123,15.123 )$

Quizplus · Accepted Answer

The confidence interval for the mean difference of matched-pairs data is calculated using the differences between each pair of observations, then finding the mean and standard deviation of those differences, and finally applying the formula for the confidence interval. Given the data sets A and B, we first calculate the differences (A - B) for each pair, then compute the mean difference, the standard deviation of the differences, and use the t-distribution (since the population standard deviation is unknown and the sample size is small) to find the 99% confidence interval. The correct interval, based on these calculations, is (-4.502, 2.622).

Construct and Interpret Confidence Intervals About the Population Mean Difference 99%99 \%99%

Construct and Interpret Confidence Intervals About the Population Mean Difference $99 \%$