Construct a 95% confidence interval for data sets A and B. Data sets A and B are random and dependent, and the populations are normally distributed. Round to the nearest tenth. $$\begin{array} { c | l l l l l }
\mathrm { A } & 30 & 28 & 47 & 43 & 31 \
\hline \mathrm { B } & 28 & 24 & 25 & 35 & 22
\end{array}$$ 2
A)(-0.7, 18.7)
B)(-1.3, 9.0)
C)(-0.1, 12.8)
D)(-15.3, 15.4)

Question

Construct a 95% confidence interval for data sets A and B. Data sets A and B are random and dependent, and the populations are normally distributed. Round to the nearest tenth. $$\begin{array} { c | l l l l l } 
\mathrm { A } & 30 & 28 & 47 & 43 & 31 \
\hline \mathrm { B } & 28 & 24 & 25 & 35 & 22
\end{array}$$ 2
A)(-0.7, 18.7)
B)(-1.3, 9.0)
C)(-0.1, 12.8)
D)(-15.3, 15.4)

Quizplus · Accepted Answer

To construct a 95% confidence interval for dependent data sets A and B, we first calculate the differences between each pair of observations. Then, we find the mean ($\bar{d}$) and standard deviation (s) of these differences. The formula for the confidence interval is $\bar{d} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}$, where $t_{\alpha/2}$ is the t-score for 95% confidence with $n-1$ degrees of freedom (here, $n=5$, so $n-1=4$), and $n$ is the number of pairs.Differences (A-B): 2, 4, 22, 8, 9. Mean ($\bar{d}$) = 9. Standard deviation (s) ≈ 7.1. Using a t-score of approximately 2.776 (for 95% confidence and 4 degrees of freedom), the confidence interval is calculated as follows:$$9 \pm 2.776 \times \frac{7.1}{\sqrt{5}} \approx 9 \pm 8.7$$Rounding to the nearest tenth gives us a confidence interval of (-0.7, 18.7).

Construct a 95% Confidence Interval for Data Sets a and B