1. Consider the partially completed one-way ANOVA summary table below.

a) Complete the remaining entries in the table. b) How many population means are being tested? c) Using =0.05, what conclusions can be made concerning the population means?(H0, H1)		Source	Sum of Squares	Degrees of Freedom	Mean Sum of Squares	F
Between	?	5	?	?
Within	72	?	?
Total	197	17

2. Consider the partially completed one-way ANOVA summary table below.

a) Complete the remaining entries in the table. b) How many population means are being tested? c) Using =0.01, what conclusions can be made concerning the population means?(H0, H1)		Source	Sum of Squares	Degrees of Freedom	Mean Sum of Squares	F
Between	188	?	?	?
Within	?	10	?
Total	258	14

3.

Student A	Student B	Student C
	291	310	267
	295	289	265
	289	297	285
	326	285	279
			279

a. Perform a one-way ANOVA using

=0.05

to determine if there is a difference in the minutes of activity of these three students. Determine the null and alternative hypotheses.

Determine the appropriate test statistic

Determine the p-value

State the proper conclusion.

b. If warranted, perform a multiple comparison test to determine which pairs are different using

=0.05.

Compare students A and B. Choose the correct answer below.

A.

Since

xAxB>CRA,B, conclude that the means for students A and B are different.

B.

Since

xAxB>CRA,B, conclude that the means for students A and B are not different.

C.

Since

xAxB

D.

Since

xAxB

E.

The multiple comparison test is not warranted.

Compare students A and C. Choose the correct answer below.

A.

Since xAxC>CRA,C, conclude that the means for students A and C are different

B.

Since xAxC

C.

Since xAxC>CRA,C, conclude that the means for students A and C are not different.

D.

Since xAxC

E.

The multiple comparison test is not warranted.

Compare students B and C. Choose the correct answer below.

A.

Since xBxC>CRB,C, conclude that the means for students B and C are different.

B.

Since xBxC

C.

Since xBxC

D.

Since xBxC>CRB,C, conclude that the means for students B and C are not different.

E.

The multiple comparison test is not warranted.

4.

Block	Sample 1	Sample 2	Sample 3
1	8	4	3
2	4	4	2
3	7	1	2
4	13	10	5

a) Calculate the total sum of squares (SST).

SST=

b) Partition the total sum of squares (SST) into its three components.

SSB=

SSBL=

SSE=

c) Using

=0.05,

what conclusions can be made about the population means? What are the correct null and alternative hypotheses?

A.

H0:

Not all the 's are equal

H1:

1=2=3

B.

H0:

1=2=3

H1:

123

C.

H0:

1=2=

H1:

Not all the 's are equal

D.

H0:

123

H1:

1=2=3

What is the test statistic?

Fx=

What is the critical value?

F=

What is the correct conclusion?

A.

Do not reject

H0.

There is no significance difference between the means.

B.

Reject

H0.

There is a significance difference between the means.

C.

Reject

H0.

There is no significance difference between the means.

D.

Do not reject

H0.

There is a significance difference between the means.

d) Was the blocking effective? Why or why not? What are the correct null and alternative hypotheses?

A.

H0:

BL1=BL2=BL3=BL4

H1:

BL1BL2BL3BL4

B.

H0:

BL1=BL2=BL3=BL4

H1:

Not all the BL's are equal

C.

H0:

BL1BL2BL3BL4

H1:

BL1=BL2=BL3=BL4

D.

H0:

Not all the BL's are equal

H1:

BL1=BL2=BL3=BL4

What is the test statistic?

FBL=

What is the critical value?

F=

What is the correct conclusion?

A.

The blocking factor was effective because H0 was rejected.

B.

The blocking factor was effective because H0 was not rejected.

C.

The blocking factor was not effective because H0 was rejected.

D.

The blocking factor was not effective because H0 was not rejected

5. With MSE=1.90, Fx=14.77, and F=3.490,

the conclusion for a randomized block ANOVA of the accompanying data is that at least one of the means is different. Determine which sample means are different using =0.05

Block	Sample 1	Sample 2	Sample 3	Sample 4
1	4	3	9	8
2	5	4	9	3
3	3	2	7	3
4	5	3	10	3
5	5	5	8	3

Let 1, 2, 3,and 4 be the means of samples 1, 2, 3, and 4, respectively. Calculate the absolute value of the difference between each pair of means.

12=

13=

14=

23=

24=

34=

What is the critical range, CR, for this randomized block ANOVA?

CR=

Which sample means are different?

A.

The means for samples1and2andsamples2and3 are different.

B.

The means for samples2and3 are different.

C.

The means for samples3and4 are different.

D.

The means for samples1and3,2and3,and3and4 are different.

E.

The means for samples1and2andsamples2and4 are different.

F.

The means for samples2and3andsamples3and4 are different.

6. Researchers would like to investigate the impact that octane has on gas mileage. The accompanying table shows the gas mileage for six cars that were driven 1,000 miles with three different grades of gasoline, 87, 89, and 93 octane. The gas mileage was recorded for each octane level. Each car was tested with all three gasoline grades.

Car	87 Octane	89 Octane	93 Octane
A	30.4	24.2	27.9
B	25.1	28.5	28.9
C	33.3	24.8	29.5
D	32.7	27.3	29.1
E	22.2	31.4	22.9
F	30.0	23.1	31.8

a. Using

=0.05,

does the octane level appear to have an effect on the gas mileage?What are the correct hypotheses to test for differences in the mileage for the octane levels?

A.

H0:

Not all the 's are equal.

H1:

87=89=93

B.

H0:

87=89=93

H1:

All the 's are different.

C.

H0:

87=89=93

H1:

Not all the 's are equal.

D.

H0:

All the 's are different.

H1:

87=89=93

Determine the test statistic.

Fx=

The p-value is

=

State the conclusion about the population means

What are the correct hypotheses to test for differences in the block means?

A.

H0:

A=B=C=D=E=F

H1:

Not all the 's are equal.

B.

H0:

Not all the 's are equal.

H1:

A=B=C=D=E=F

C.

H0:

All the 's are different.

H1:

A=B=C=D=E=F

D.

H0:

A=B=C=D=E=F

H1:

All the 's are different.

Determine the test statistic.

FBL=

What is the p-value?

=

State the conclusion about the blocking.

If warranted, determine which pairs of octanes were different using

=0.05.

The mileages for were significantly different