Followup Tests of Temperature Main EffectsTukey’s Follow Up to two-way ANOVA In Class Work General Linear Model: Chem versus Temp, Pressure Factor Type Levels ValuesTemp fixed 3 150, 160, 170Pressure fixed 3 200, 215, 230Analysis of Variance for Chem, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PTemp 2 0.30111 0.30111 0.15056 8.47 0.009Pressure 2 0.76778 0.76778 0.38389 21.59 0.000Temp*Pressure 4 0.06889 0.06889 0.01722 0.97 0.470Error 9 0.16000 0.16000 0.01778Total 17 1.29778S = 0.133333 R-Sq = 87.67% R-Sq(adj) = 76.71%Temp23021520090.890.690.490.290.017016015090.890.690.490.290.0Pressure150160170Temp200215230PressureInteraction Plot (fitted means) for ChemFollowup Tests of Temperature Main EffectsTukey 95.0% Simultaneous Confidence IntervalsResponse Variable ChemAll Pairwise Comparisons among Levels of TempTemp = 150 subtracted from:Temp Lower Center Upper -----+---------+---------+---------+-160 -0.3817 -0.1667 0.04834 (-------*--------)170 -0.0650 0.1500 0.36501 (--------*--------) -----+---------+---------+---------+- -0.25 0.00 0.25 0.50Temp = 160 subtracted from:Temp Lower Center Upper -----+---------+---------+---------+-170 0.1017 0.3167 0.5317 (--------*-------) -----+---------+---------+---------+- -0.25 0.00 0.25 0.50Followup Tests of Pressure Main EffectsTukey 95.0% Simultaneous Confidence IntervalsResponse Variable ChemAll Pairwise Comparisons among Levels of PressurePressure = 200 subtracted from:Pressure Lower Center Upper +---------+---------+---------+------215 0.1017 0.3167 0.53168 (-----*-----)230 -0.3983 -0.1833 0.03168 (-----*-----) +---------+---------+---------+------ -0.70 -0.35 0.00 0.35Pressure = 215 subtracted from:Pressure Lower Center Upper +---------+---------+---------+------230 -0.7150 -0.5000 -0.2850 (-----*-----) +---------+---------+---------+------ -0.70 -0.35 0.00 0.351. Why is it appropriate to conduct Tukey’s follow-up test.The test for interaction is insignificant (p-value=.47), and we have significant temperature main effect (p-value=.009) and a significant pressure main effect (p-value = 0.000). Thus, we can perform a follow-up test on each of the main effects todetermine which levels of these factors give different mean chemical yields.2. Is there a temperature that yields a significantly higher mean chemical yield than the others? Interpret the Tukey confidence intervals.The 95% Tukey CI’s show that the only significant difference in mean chemical yield between the levels of temperature is that for 170 degrees and 160 degrees. That is, the Tukey CI for the mean chemical yield at 170 minus the mean chemical yield at 160 is the only one does not contain zero. Thus, we are 95% confident that the mean chemical yield at 170 degrees is between .1017 and .5317 greater than the mean chemical yield at 160 degrees. 3. How much pressure ought to be applied to get a significantly greater mean chemical yield than the others? Use CI’s to estimate how much higher the mean chemical yield is at this desired temperature.From the 95% Tukey CI’s for the levels of pressure, we see that a pressure of 215 pascals yields a significantly higher mean chemical yield than when the pressure is ateither 200 or 230 pascals. In other words, all of the CI’s comparing the mean chemical yield for pressure at 215 pascals with the others do not contain zero. Thus, we are 95% confident that the mean chemical yield using a pressure of 215 pascals is between .03 and .4 greater than the mean chemical yield at 200 pascals, and between .3 and .72 greater than the mean chemical yield at 230 pascals.4. An executive at the Yummy Chemical Company is interested in changing the process to produce greater amounts of the chemical we have been studying. Currently, the process uses a pressure of 215 pascals and a temperature of 160 degrees. What do you recommend to the executive about changing the process? Give a CI of how much the executive can expect the mean chemical yield to increase if your recommendation is used.Tukey’s follow-up analysis suggests that the temperature ought to be changed from 160 to 170 degrees. From the Tukey CI (0.1017, 0.5317), we can say that we are95% confident that the mean yield of the chemical process will increase by between .1017 and