Question

The following data are from a completely randomized design. In the following calculations, use

α = 0.05.

	Treatment 1	Treatment 2	Treatment 3
	64	82	69
	48	73	53
	55	89	61
	37	68	45
xj	51	78	57
sj2	130.00	87.33	106.67

Find the value of the test statistic. (Round your answer to two decimal places.)___

Find the p-value. (Round your answer to three decimal places.)

p-value = ____

+Use Fisher's LSD procedure to determine which means are different.

Find the value of LSD. (Round your answer to two decimal places.)

LSD = ____

Find the pairwise absolute difference between sample means for each pair of treatments
x₁ − x₂₌

x₁ − x₃=

x₂ − x₃₌

To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, a chemical company obtained the following data on the time (in minutes) needed to mix the material.

Manufacturer
1	2	3
21	27	20
26	26	18
23	30	23
18	33	23

Find the value of the test statistic. (Round your answer to two decimal places.)___

Find the p-value. (Round your answer to three decimal places.)

p-value = ____

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

Find the value of LSD. (Round your answer to two decimal places.)

LSD = ____

Find the pairwise absolute difference between sample means for manufacturers 1 and 3.

x₁ − x₃ =___

Answer 1

1)

Applying ANOVA:

value of the test statistic =7.44

p value =0.012

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

16.62

Difference	Absolute Value	Conclusion
x2-x1	27.00	significant difference
x3-x1	6.00	not significant difference
x3-x2	21.00	significant difference

2)

test statistic =	8.34
p value is less than 0.009

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

4.83

x₁ − x₃ = 1 : not significant difference