Solution Found!
The article “Simulation of the Hot Carbonate Process for
Chapter 5, Problem 1E(choose chapter or problem)
The article “Simulation of the Hot Carbonate Process for Removal of \(\rm{CO}_2\) and \(\rm{H}_2 \rm{S}\) from Medium Btu Gas” (K. Park and T. Edgar, Energy Progress, 1984: 174-180) presents an equation used to estimate the equilibrium vapor pressure of \(\rm{CO}_2\) in a potassium carbonate solution. The actual equilibrium pressure (in kPa) was measured in nine different reactions and compared with the value estimated from the equation. The results are presented in the following table:
\(\begin{array}{crrr} \hline \text { Reaction } & \text { Estimated } & \text { Experimental} & \text{Difference } \\ \hline 1 & 45.10 & 42.95 & 2.15 \\ 2 & 85.77 & 79.98 & 5.79 \\ 3 & 151.84 & 146.17 & 5.67 \\ 4 & 244.30 & 228.22 & 16.08 \\ 5 & 257.67 & 240.63 & 17.04 \\ 6 & 44.32 & 41.99 & 2.33 \\ 7 & 84.41 & 82.05 & 2.36 \\ 8 & 150.47 & 149.62 & 0.85 \\ 9 & 253.81 & 245.45 & 8.36 \\ \hline \end{array}\)
Find a 95% confidence interval for the mean difference between the estimated and actual pressures.
Questions & Answers
QUESTION:
The article “Simulation of the Hot Carbonate Process for Removal of \(\rm{CO}_2\) and \(\rm{H}_2 \rm{S}\) from Medium Btu Gas” (K. Park and T. Edgar, Energy Progress, 1984: 174-180) presents an equation used to estimate the equilibrium vapor pressure of \(\rm{CO}_2\) in a potassium carbonate solution. The actual equilibrium pressure (in kPa) was measured in nine different reactions and compared with the value estimated from the equation. The results are presented in the following table:
\(\begin{array}{crrr} \hline \text { Reaction } & \text { Estimated } & \text { Experimental} & \text{Difference } \\ \hline 1 & 45.10 & 42.95 & 2.15 \\ 2 & 85.77 & 79.98 & 5.79 \\ 3 & 151.84 & 146.17 & 5.67 \\ 4 & 244.30 & 228.22 & 16.08 \\ 5 & 257.67 & 240.63 & 17.04 \\ 6 & 44.32 & 41.99 & 2.33 \\ 7 & 84.41 & 82.05 & 2.36 \\ 8 & 150.47 & 149.62 & 0.85 \\ 9 & 253.81 & 245.45 & 8.36 \\ \hline \end{array}\)
Find a 95% confidence interval for the mean difference between the estimated and actual pressures.
ANSWER:Step 1 of 4
Given:
The sample number of reactions is n = 9.
Let x represent the estimated values from the equation.
Let y represent the experimental values from the equation.
Let d represents the difference between estimated and experimental values; that is; \(d=x_{i}-y_{i}\).
The mean difference between the estimated and actual pressures is given as:
\(\begin{aligned} \bar{d} & =\frac{\sum\left(x_{i}-y_{i}\right)}{n} \\ & =\frac{2.15+5.79+5.67+16.08+\ldots+0.85+8.36}{9} \\ & =6.7367 \end{aligned}\)
Therefore, the mean difference between the estimated and actual pressures is 6.7367.