Question

To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material 25 31 29 27 Manufacturer 2 31 29 34 30 17 16 20 19 a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use α .05 Compute the values below (to 2 decimals, if necessary) Sum of Squares, Treatment Sum of Squares, Error Mean Squares, Treatment Mean Squares, Error Calculate the value of the test statistic (to 2 decimals) The p-value is less than 01 What is your conclusion? Conclude the mean time needed to mix a batch of material is not the same for all manufacturers

Answer 1

applying ANOVA on above data:

X1 25 31 X2 31 X3 17 16 Total 73 83 30 12 Total 2X Average-X-XJnz Total-EX- 112 28.0000 3156 6.6667 124 72 18.0000 1306 3.3333 31.0000 grand mean Xgrand 25.6667 4.6667 Total observation number of groups 12 between groups degree of freedom dfbg k-1- within groups degree of freedom dfwg-N-k - Total degree of freedom Tota 28.0000 31.0000 18.0000 6.667 4.667 3.333 Si n(XXgand)(n-1)s' 21.78 113.78 235.11 20.00 14.00 10.00 44.0000 total 370.6667 sum of square between groups SSG 2(n-1) S SSG+SSE 370.6667 44.0000 414.6667 sum of square within groups SSE total sum of square SST Summary table Source of variation between within total df 2.0000 9.0000 11.0000 MS 185.33 4.89 37.91 370.667 44.000 414.667

from above

a)

sum of square; treatment=	370.67
sum of square; error=	44.00
mean square; treatment=	185.33
mean square; error=	4.89

test statistic =

37.91

b)

Fisher's (LSD) for group i and j =                  (tN-k)*(sp*√(1/ni+1/nj)           =

3.54

(try 3.52 or 3.53 if this comes wrong)