To test whether themean time needed to mix a batch of material is the same formachines produced by three manufacturers, the Jacobs ChemicalCompany obtained the following data on the time (in minutes) neededto mix the material.

Manufacturer
	1	2	3
	21	27	24
	27	24	18
	21	30	24
	18	27	18

1. Use these data to test whetherthe population mean times for mixing a batch of material differ forthe three manufacturers. Use = .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 Selectless than .01between .01 and.025between .025 and .05between .05 and .10greater than .10
   
   What is your conclusion?
   
   SelectConclude the mean time needed to mix a batch of material isnot the same for all manufacturersDo not reject the assumption thatmean time needed to mix a batch of material is the same for allmanufacturers
   
2. At the = .05 level ofsignificance, use Fisher's LSD procedure to test for the equalityof 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 andthe mean time for manufacturer 3?
   
   SelectCannot conclude there is a difference in the mean time forthese manufacturersThese manufacturers have different meantimes