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.

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

. At the a= .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).

	1	2	3
	15	35	17
	21	33	16
	19	38	20
	17	34	19

Answer 1

	Group 1	Group 2	Group 3	Total
Sum	72	140	72	284
Count, n	4	4	4	12
Average, sum/n	18	35	18
Sum of square, Ʃ(xᵢ-x̅)²	20	14	10

Number of treatment, k = 3
Total sample Size, N = 12
      
df(treatment) = k-1 =   2
df(error) = N-k =   9
df(total) = N-1 =  11
      
SS(treatment) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N =  770.6667
SS(error) = SS1 + SS2 + SS3 =   44
SS(total) = SS(treatment) + SS(error) =   814.6667
      
MS(treatment) = SS(treatment)/df(treatment) =  385.3333
MS(error) = SS(error)/df(error) =  4.8889
      

Test statistic:
F = MS(treatment)/MS(error) =   78.82
p-value = F.DIST.RT(78.82, 2, 9) = 0.0000

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b) Critical t value at df = N-k = 9, t_c = T.INV.2T(0.05, 9) = 2.262

LSD = t* √(2*MS(error)/n) = 2.262 *√(2*4.8889/4) = 3.54