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.

Manufacturer
	1	2	3
	21	34	16
	27	32	15
	25	37	19
	23	33	18

a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a=0.05.

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, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10)

What is your conclusion?

________ (Conclude the mean time needed to mix a batch of material is not the same for all manufacturers, Do not reject the assumption that mean time needed to mix a batch of material is the same for all manufacturers)

b. At the a=0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3.

Calculate Fisher's LSD Value (to 2 decimals).

___________

What is your conclusion about the mean time for manufacturer 1 and the mean time for manufacturer 3 ?

(These manufacturers have different mean times, Cannot conclude there is a difference in the mean time for these manufacturers)

Answer 1

a)

sum of square; treatment=	584.00
sum of square; error=	44.00
mean square; treatment=	292.00
mean square; error=	4.89

test statistic =

59.73

The p value is less than .01

Conclude the mean time needed to mix a batch of material is not the same for all manufacturers,

b)

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

3.54

These manufacturers have different mean times