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.

Manufacture
1	2	3
18	30	24
27	24	18
24	33	27
21	27	21

a. Compute the values below (to 2 decimals, if necessary).

Sum of Squares, Error
Mean Squares, Error
Fisher's LSD Value

b. Use Fisher's LSD procedure to develop a 95% confidence interval estimate of the difference between the means for manufacturer 1 and manufacturer 2. Round to two decimal places. Enter negative values as negative numbers.
to

Answer 1

Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array):

Source	SS	df	MS	F	P value
Between	96.000	2	48.00	3.2000	0.089
Within	135.000	9	15.00
Total	231.000	11

a)

sum of sq; error=

135.00

mean square; error=

15.00

critical value of t with 0.05 level and N-k=9 degree of freedom=				tN-k=	2.262
Fisher's (LSD) for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =					6.19

b)

95% confidence interval estimate of the difference between the means for manufacturer 1 and manufacturer 2 =(x1-x2) -/+ LSD = -12.19 to 0.19