Question

QUESTION 10

1. Questions 10 through 13 refer to the following:

   Using the partially completed analysis of variance and table of means provided below, answer the following questions. Use the .05 significance level. All three groups have the same sample size.

   Source	SS	df	MS	F
   Treatment				3.9302
   Error			9.03
   Total		26

   	Group
   	A	B	C
   sample mean	278.3	275.4	274.5

   Find the value of LSD for comparing Groups A and B.

QUESTION 11

1. Is the difference between groups A and B significant?

   		yes
   		no
   		maybe?
   		Antidisestablishmentarianism

QUESTION 12

1. What's the value of SSTR?

QUESTION 13

1. What's the value of SSE?

Answer 1

QUESTION 10

Source	SS	df	MS	F
Treatment	70.98	2	35.49	3.9302
Error	216.72	24	9.03
Total	287.70	26

DONE

Concept Base

Degrees of freedom

Treatment: Number if treatments (groups) – 1 = 3 – 1 = 2

Error: df for Total – df for Treatment = 26 (given) – 2 = 24

F = MSTr/MSE

So, MSTr = F x MSE = 3.9302 x 9.03 = 35.49

MSTr = SSTr/df, or

SSTr = MSTr x df = 35.49 x 2 = 70.98

Similarly, SSE = 9.03 (given) x 24 = 216.72

SST = SSTr + SSE = 70.98 + 216.72 = 287.70.

Value of LSD for comparing Groups A and B.

QUESTION 11

Value of LSD for comparing Groups A and B

Concept Base

Let n1 and n2 be the sample sizes for obtaining X1bar and X2bar.
LSDcrit = t(α/2)√[MSW{(1/n1) + (1/n2)}], where
t(α/2) = upper (α/2) percent point of t-distribution with
degrees of freedom = DF of MSW i.e., Error or Residual MS of ANOVA
Decision: The difference, d = |X1bar - X2bar| is significant if
d > LSDcrit, as given above.

Now, the calculations

d = 278.3 – 275.4 = 2.9

n1 = n2 = 9

t(α/2) = upper 2.5% percent point of t-distribution with 24 degrees of freedom

= 2.064 [from Standard t-distribution Tables]

MSW = 9.03 [from ANOVA Table]

{(1/n1) + (1/n2)} = 2/9 = 0.2222

LSDcrit = 2.064√(9.03 x 0.2222)

= 2.923

Here the difference between d and LSDcrit is marginal. Hence, we conclude that the difference between the means of Group A and Group B is not significant. Answer

QUESTION 12

SSTR = 70.98 [from ANOVA Table] Answer

QUESTION 13

SSE = 216.72 [from ANOVA Table] Answer

DONE