Question

Information for questions #14-20.

Complete the following ANOVA table and then answer the questions that follow.  The ANOVA test was conducted using a significance level of 0.05.

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1030964	3	c	e	0.074	f
Within Groups	2561191	b	d
Total	a	23

14) In the ANOVA table above, what is the value of (a)?

A)  3,591,155

B)  1,030,964

C)  2,561,191

D)  1,530,227

E)  3,592,155

15) In the ANOVA table above, what is the value of (b)?

A)  23

B)  26

C)  20

D)  3

E)  24

16) In the ANOVA table above, what is the value of (c)?

A)  343,654.67

B)  515,482.00

C)  42,956.83

D)  39,652.46

E)  44,824.52

17) In the ANOVA table above, what is the value of (d)?

A)  111,356.13

B)  98,507.35

C)  106,716.29

D)  1,280,595.50

E)  128,059.55

18) In the ANOVA table above, what is the value of (e)?

A)  2.68

B)  4.63

C)  0.44

D)  0.37

E)  0.04

19) In the ANOVA table above, what is the value of (f)?

A)  14.17

B)  3.10

C)  8.66

D)  3.86

E)  None of the above.

20) In this ANOVA test, do you reject of fail to reject H0?

A)  Reject

B)  Fail to reject H0

Answer 1

Anova

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1030964	3	343,654.67	2.68	0.074	3.10
Within Groups	2561191	20	128059.55
Total	3,592,155	23

a) Here, Total SS = SS( Between groups ) + SS( Within Groups )
= 1030964 + 2561191
  =  3,592,155 i.e. option E.

b) df ( Total ) = df( Between groups ) + df( Within Groups )
Thus, df( Within Groups ) = 23 - 3 = 20  i.e. option C.

c) MS( Between groups ) = SS( Between groups ) / df( Between groups )
=  1030964 / 3
= 343,654.67 i.e. option A.

d) MS( Within groups ) = SS( Within groups ) / df( Within groups )
= 2561191 / 20
= 128059.55 i.e. option E.

e) F = MS( Between groups ) / MS( Within groups )
=  343,654.67 /  128059.55
   = 2.68 i.e option A.

f) F crit = F ( , k-1, n-k ) = F (0.05, 3, 20) = 3.10 i.e option B.

g) Since F < F-crit, we fail to reject Ho at 5% l.o.s.

Hope this answers your query!