We are interested in comparing the amount of acidity in sour cream with respect to using different starters for making the sour cream. The data is given below.

   Acidity Starter
1     8.04       3
2     6.61       2
3    11.99       4
4     7.78       5
5     8.40       1
6     9.58       4
7     6.58       5
8     6.66       1
9     5.34       3
10    7.92       2
11    7.98       5
12    7.98       3
13    8.98       2
14    7.94       1
15   11.32       4
16    9.74       2
17    9.46       1
18    9.14       3
19   12.00       4
20    9.32       5
21    9.66       1
22   11.28       4
23    8.04       5
24    8.12       2
25    6.72       3

Answer the following questions:

1. (3 points) Complete the following table:
    

   Source	df	Sum of Squares	MS	F-value	p-value
   Group		44.14
   Error		27.68		N/A	N/A
   Total			N/A	N/A	N/A

2. (4 points) What are the assumptions that we should check before conducting the hypothesis test?
   What is the distribution of the test statistic under H₀ (state the name of the distribution and the degrees of freedom, if applicable)?
    
3. (5 points) Using tables or R, report the p-value and state your conclusion for the hypothesis test. Interpret the conclusion in the context of the problem.
    
4. (5 points) Regardless of the conclusion on the previous question, we perform Tukey's HSD. The output is shown below:

 

1. Answer the following questions:
    
   1. What is the purpose of performing TukeyHSD?
       
   2. Why are there 10 rows in the output?
       
   3. From the output, find out the four rows that exhibit a discovery.  Interpret the result in the context of the problem.

 

> TukeyHSD(aov (sc.dat$Aciditywas.factor(sc.dat$Starter))) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = sc.dat$Acidity as.factor(sc.dat$Starter)) $ as.factor (sc.dat$Starter) diff lwr p adj upr 2-1 -0.150 -2.3763621 2.076362 0.9995975 3-1 -0.980 -3.2063621 1.246362 0.6841202 4-1 2.810 0.5836379 5.036362 0.0092748 5-1 -0.484 -2.7103621 1.742362 0.9645415 3-2 -0.830 -3.0563621 1.396362 0.7965407 4-2 2.960 0.7336379 5.186362 0.0059139 5-2 -0.334 -2.5603621 1.892362 0.9909443 4-3 3.790 1.5636379 6.016362 0.0004772 5-3 0.496 -1.7303621 2.722362 0.9613274 5-4 -3.294 -5.5203621 -1.067638 0.0021494