[13 marks] A study investigated the the effect of water based firebed cooling on a residential wood pellet boiler. Recent development of residential wood pellet boilers has focused on the release of inorganic aerosols. In the study, the boiler was run several times both with and without firebed cooling. For each run the flame temperature (C) and total suspend particles (mg/Nm3) were measured. Download the file Firebed.csv, which contains the following variables: Cooling - Was firebed cooling was used? (On/Off) FT - Flame temperature TSP - Total suspended particles (a) Is there any evidence of a difference in the expected flame temperature between the boiler operating with firebed cooling compared to operating without firebed cooling? i. Construct an appropriate plot to assess whether the data is consistent with the assumption(s) required to apply these methods? ii. State the null and alternative hypothesis that you wish to test. Report the test statistic and P-value from Python. What do you conclude. [5 marks] (b) Provide a 95% confidence interval (using Welch degrees of freedom) for the difference (OFF - ON) in expected total suspended particles. (c) Provide a 90% confidence interval for the expected total suspend particles when firebed cooling is used. [3 marks] \begin{tabular}{|r|r|} \hline \multicolumn{2}{|l|}{ FEI } \\ \hline FEI & Eta_HTHS \\ \hline 1.51 & 3.51 \\ \hline 1.69 & 3.49 \\ \hline 1.8 & 3.62 \\ \hline 1.9 & 3.7 \\ \hline 2 & 3.65 \\ \hline 2.01 & 3.5 \\ \hline 2.2 & 3.46 \\ \hline 2.54 & 3.02 \\ \hline 2.6 & 3 \\ \hline 2.6 & 3.03 \\ \hline 2.7 & 3.04 \\ \hline 2.73 & 2.95 \\ \hline 2.79 & 3.08 \\ \hline 2.8 & 3 \\ \hline 2.9 & 3.19 \\ \hline 3 & 2.9 \\ \hline 3.05 & 2.67 \\ \hline 3.1 & 2.9 \\ \hline 3.41 & 3.02 \\ \hline \end{tabular} Firebed \begin{tabular}{|l|l|l|} \hline Cooling & FT & TSP \\ \hline Off & 785.8724891 & 17.08145207 \\ \hline Off & 786.8501239 & 12.97628334 \\ \hline Off & 764.4880366 & 11.62975799 \\ \hline Off & 764.5982251 & 14.99460429 \\ \hline Off & 779.7449961 & 16.56468048 \\ \hline Off & 776.1461558 & 17.13700392 \\ \hline Off & 739.5256283 & 15.60135337 \\ \hline Off & 804.8289263 & 17.81024242 \\ \hline Off & 738.7401368 & 14.58445165 \\ \hline Off & 767.7566082 & 6.727850378 \\ \hline Off & 760.0315258 & 18.22799455 \\ \hline Off & 716.6671471 & 16.51226214 \\ \hline Off & 812.7143412 & 13.43555397 \\ \hline Off & 734.403879 & 15.29316816 \\ \hline Off & 758.450688 & 12.55518423 \\ \hline Off & 773.9842117 & 14.73733535 \\ \hline Off & 688.6824091 & 16.0241901 \\ \hline Off & 766.5182957 & 13.3373858 \\ \hline Off & 818.9413956 & 14.8076318 \\ \hline Off & 711.3332471 & 15.74761897 \\ \hline Off & 752.9665672 & 17.88310595 \\ \hline Off & 747.1324152 & 19.28045463 \\ \hline Off & 725.9272784 & 19.24758319 \\ \hline \end{tabular} \begin{tabular}{|l|r|r|} \hline On & 738.8106189 & 13.82193162 \\ \hline On & 746.4720277 & 10.77635601 \\ \hline On & 775.8057022 & 13.06490733 \\ \hline On & 764.1912182 & 11.66403407 \\ \hline On & 727.923597 & 15.32366866 \\ \hline On & 744.6652638 & 14.26320016 \\ \hline On & 795.9234455 & 13.66125801 \\ \hline On & 747.6626439 & 11.19460133 \\ \hline On & 774.5290416 & 11.72375902 \\ \hline On & 729.4702301 & 13.77550769 \\ \hline On & 751.120347 & 13.41313375 \\ \hline On & 814.484767 & 11.86499443 \\ \hline On & 772.6271101 & 8.523996799 \\ \hline On & 777.2047974 & 14.08306573 \\ \hline On & 785.6629968 & 13.38576732 \\ \hline On & 733.5780437 & 11.15575209 \\ \hline On & 781.6800843 & 12.71151973 \\ \hline \end{tabular} [13 marks] A study investigated the the effect of water based firebed cooling on a residential wood pellet boiler. Recent development of residential wood pellet boilers has focused on the release of inorganic aerosols. In the study, the boiler was run several times both with and without firebed cooling. For each run the flame temperature (C) and total suspend particles (mg/Nm3) were measured. Download the file Firebed.csv, which contains the following variables: Cooling - Was firebed cooling was used? (On/Off) FT - Flame temperature TSP - Total suspended particles (a) Is there any evidence of a difference in the expected flame temperature between the boiler operating with firebed cooling compared to operating without firebed cooling? i. Construct an appropriate plot to assess whether the data is consistent with the assumption(s) required to apply these methods? ii. State the null and alternative hypothesis that you wish to test. Report the test statistic and P-value from Python. What do you conclude. [5 marks] (b) Provide a 95% confidence interval (using Welch degrees of freedom) for the difference (OFF - ON) in expected total suspended particles. (c) Provide a 90% confidence interval for the expected total suspend particles when firebed cooling is used. [3 marks] \begin{tabular}{|r|r|} \hline \multicolumn{2}{|l|}{ FEI } \\ \hline FEI & Eta_HTHS \\ \hline 1.51 & 3.51 \\ \hline 1.69 & 3.49 \\ \hline 1.8 & 3.62 \\ \hline 1.9 & 3.7 \\ \hline 2 & 3.65 \\ \hline 2.01 & 3.5 \\ \hline 2.2 & 3.46 \\ \hline 2.54 & 3.02 \\ \hline 2.6 & 3 \\ \hline 2.6 & 3.03 \\ \hline 2.7 & 3.04 \\ \hline 2.73 & 2.95 \\ \hline 2.79 & 3.08 \\ \hline 2.8 & 3 \\ \hline 2.9 & 3.19 \\ \hline 3 & 2.9 \\ \hline 3.05 & 2.67 \\ \hline 3.1 & 2.9 \\ \hline 3.41 & 3.02 \\ \hline \end{tabular} Firebed \begin{tabular}{|l|l|l|} \hline Cooling & FT & TSP \\ \hline Off & 785.8724891 & 17.08145207 \\ \hline Off & 786.8501239 & 12.97628334 \\ \hline Off & 764.4880366 & 11.62975799 \\ \hline Off & 764.5982251 & 14.99460429 \\ \hline Off & 779.7449961 & 16.56468048 \\ \hline Off & 776.1461558 & 17.13700392 \\ \hline Off & 739.5256283 & 15.60135337 \\ \hline Off & 804.8289263 & 17.81024242 \\ \hline Off & 738.7401368 & 14.58445165 \\ \hline Off & 767.7566082 & 6.727850378 \\ \hline Off & 760.0315258 & 18.22799455 \\ \hline Off & 716.6671471 & 16.51226214 \\ \hline Off & 812.7143412 & 13.43555397 \\ \hline Off & 734.403879 & 15.29316816 \\ \hline Off & 758.450688 & 12.55518423 \\ \hline Off & 773.9842117 & 14.73733535 \\ \hline Off & 688.6824091 & 16.0241901 \\ \hline Off & 766.5182957 & 13.3373858 \\ \hline Off & 818.9413956 & 14.8076318 \\ \hline Off & 711.3332471 & 15.74761897 \\ \hline Off & 752.9665672 & 17.88310595 \\ \hline Off & 747.1324152 & 19.28045463 \\ \hline Off & 725.9272784 & 19.24758319 \\ \hline \end{tabular} \begin{tabular}{|l|r|r|} \hline On & 738.8106189 & 13.82193162 \\ \hline On & 746.4720277 & 10.77635601 \\ \hline On & 775.8057022 & 13.06490733 \\ \hline On & 764.1912182 & 11.66403407 \\ \hline On & 727.923597 & 15.32366866 \\ \hline On & 744.6652638 & 14.26320016 \\ \hline On & 795.9234455 & 13.66125801 \\ \hline On & 747.6626439 & 11.19460133 \\ \hline On & 774.5290416 & 11.72375902 \\ \hline On & 729.4702301 & 13.77550769 \\ \hline On & 751.120347 & 13.41313375 \\ \hline On & 814.484767 & 11.86499443 \\ \hline On & 772.6271101 & 8.523996799 \\ \hline On & 777.2047974 & 14.08306573 \\ \hline On & 785.6629968 & 13.38576732 \\ \hline On & 733.5780437 & 11.15575209 \\ \hline On & 781.6800843 & 12.71151973 \\ \hline \end{tabular}