1. [R] The yield of a chemical process is being studied. The two factors of interest are temperature and pressure. There levels of each factor were selected but only nine runs can be made in one day. The experimenter runs one replicate of the design on each day (the days are blocks). The data are below:
   Day 1 Day 2
   TempPressure 250 260 270 250 260 270
   Low 86.3 84 85.8 86.1 85.2 87.3
   Medium 88.5 87.3 89 89.4 89.9 91.3
   High 89.1 90.2 91.3 91.7 93.2 93.7

i) Construct the ANOVA table of the experiment. Copy/paste it here.

ii) Is there a temperature main effect? _ How about a pressure main effect? Do the temperature and pressure interact?

iii) Was it a good idea to use day as a blocking factor? _

iv) Construct plots of residuals and decide if the ANOVA assumptions are satisfied. Insert the plots below and type your conclusions regarding the assumptions.

v) Construct an interaction plot that has the pressure on the horizonal axis. Insert the plot here.

vi) If the goal is to maximize the process yield, at what pressure(s) would you recommend them to run the process? _ Does your recommendation depend on the temperature? _

2. [By hand] An experiment was conducted to investigate nisin extraction in aqueous two-phase solutions. A two-factor factorial experiment was conducted using factors A = concentration of PEG and B = concentration of Na2SO4. The following data are available:

A 13 13 15 15 13 13 15 15
B 11 11 11 11 13 13 13 13
Extraction 62.9 63.4 76.1 72.3 87.5 86.2 102.3 105.6

i) Calculate the A main effect = , the B main effect = , and the AB interaction effect = __. Show your work!

ii) Calculate the sums of squares for A main effect, B main effect, and AB interaction. Show your work!

iii) It SSE = 13.6, construct by hand the ANOVA table for this experiment.

3. Below are the scores of three rounds of golf played at three different golf courses with two types of golf clubs:
   Course
   Club Ahwatukee Karsten Foothills
   Old 90, 87, 86 91, 98, 90 88, 86, 90
   New 88, 87, 85 90, 91, 88 86, 85, 88

i) [R] Construct the ANOVA table for this experiment. Copy/paste it here.

ii) Is there a club main effect? _ How about an interaction? __

For the following two questions you may use R to get the necessary sample means, but the actual pairwise comparisons should be carried out by hand.

iii) Use Fisher’s LSD method to conduct pairwise comparisons between the three courses when using new golf clubs.

iv) Use Tukey’s method to conduct pairwise comparisons between the three courses.