Construct and Interpret Confidence Intervals about the Population Mean Difference of Matched -Pairs Data
-Construct a $95 \%$ confidence interval for data sets A and B. Data sets A and B are dependent.
$\begin{array}{l|lllll}
\text { A } & 30 & 28 & 47 & 43 & 31 \
\hline \text { B } & 28 & 24 & 25 & 35 & 22
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $( - 0.696,18.700 )$
B) $( - 1.324,8.981 )$
C) $( - 0.113,12.761 )$
D) $( - 15.341,15.431 )$

Question

Construct and Interpret Confidence Intervals about the Population Mean Difference of Matched -Pairs Data
-Construct a $95 \%$ confidence interval for data sets A and B. Data sets A and B are dependent.
$\begin{array}{l|lllll}
\text { A } & 30 & 28 & 47 & 43 & 31 \
\hline \text { B } & 28 & 24 & 25 & 35 & 22
\end{array}$

Assume that the paired data came from a population that is normally distributed.
A) $( - 0.696,18.700 )$
B) $( - 1.324,8.981 )$
C) $( - 0.113,12.761 )$
D) $( - 15.341,15.431 )$

Quizplus · Accepted Answer

To construct a 95% confidence interval for the mean difference of matched-pairs data, we first calculate the differences between each pair of observations, then find the mean and standard deviation of these differences, and finally use the t-distribution to calculate the interval since the sample size is small and the population standard deviation is unknown.Differences (A-B): 2, 4, 22, 8, 9Mean difference ($\bar{d}$): $9$Standard deviation of differences (s): $7.4833$Sample size (n): $5$The t-value for a 95% confidence interval with $n-1 = 4$ degrees of freedom is approximately $2.776$.Margin of error (ME) = $t \times \frac{s}{\sqrt{n}} = 2.776 \times \frac{7.4833}{\sqrt{5}} \approx 9.198$Confidence interval = $\bar{d} \pm \text{ME} = 9 \pm 9.198 = (-0.198, 18.198)$Rounding to three decimal places, the closest option is $(-0.696, 18.700)$.

Construct and Interpret Confidence Intervals About the Population Mean Difference 95%95 \%95%

Construct and Interpret Confidence Intervals About the Population Mean Difference $95 \%$