Question

A dairy farmer is looking at methods for transporting milk from her farm to a dairy plant. Three different methods are trialed over fourteen working days, and the daily costs of the methods (in $ 100) were as follows: Method 16.04 5.05 5.80 4.90 Method 28.82 5.59 6.36 5.85 6.75 Method 3 9.53 8.79 10.24 9.10 7.99 Box plots displaying the data are shown below: Daily Cost of Milk Transportation by Three Delivery Metho ot Cost in 100s of Dollars Delivery Method Part b) A table summarizing the data is given below. Provide the missing standard deviation to three decimal places): Method Sample size Mean Standard deviation 1 4 5.447 0.558 2 5 6.674 1.281 5 9 .130 0.838 Part c) Taking that the underlying assumptions of ANOVA hold and that the approach will be applied, what is the estimate of the common variance of the daily costs for the three delivery methods? (Give your answer to three decimal places.); Part d) Complete the ANOVA table below, giving answers to one decimal place for F-ratio and three decimal places for everything else (i.e. for SS and MS). In particular, when calculating the F-ratio, make sure you keep all intermediate steps to at least 6 decimal places in order to arrive at a final answer that is accurate to one decimal place. Source of Variation of SS M S F Factor Error Total

Answer 1

applying ANOVA on above data:

treatment 1 treatment 2 880 ന് ഗ് ഗ് treatment 3 9.53 8.79 10.24 9.1 7.99 count ni Average=l=zX;/n,- Total=zX* - SS=zX*i -(xi) Ini 5.4475 119.634 0.933 6.6740 229.2751 6.5637 9.1300 419.5927 2.8082 Grand average Xgrand=xi!N = 100.8119- 7.2007

2. A treatment 1 creatment 2 creatment 3 Total K 5.4475 6.6740 9.1300 n'(X-Xarand) 12.295 1.387 18.611 32.293 SST SS-ini-11's? 0.933075 6.56372 2.8082 10.3050 SSE df treatmer number of treatments-1= of error = N-k= df total= N-1 14-3= 14-1= MS(treatment) =SSTildf(Tr)=32.29/2= MS[error) =SSE/dfſerror)=10.3/11= test statistio F =MST/MSE - 16.15/0.94= 16.14645 0.93682 17.23542 Source SS MS 17.24 Between Within Total 32.2929 10.3050 42.60 NEW 16.146 0.9368

from above

c)

common variance =MSE =0.937

d)

Source	df	SS	MS	F
Treatment	2	32.293	16.146	17.2
Error	11	10.305	0.937
Total	13	42.598