7. To compare the driving distances of various golf balls, eight golfers were asked to hit golf balls by brands A, B, and C with their drivers. The distance for each shot was measured in yards and the accompanying table shows the distances. Complete parts a through c below.

Golfer	A	B	C
1	235	242	234
2	235	262	208
3	230	249	220
4	248	250	219
5	244	260	207
6	236	249	235
7	244	235	205
8	231	251	220

a. Using

=0.05, does there appear to be a difference in the driving yardage of the balls? What are the correct hypotheses to test for differences in the driving distance?

A.

H0:

A=B=C

H1:

All the 's are different.

B.

H0:

Not all the 's are equal.

H1:

A=B=C

C.

H0:

All the 's are different.

H1:

A=B=C

D.

H0:

A=B=C

H1:

Not all the 's are equal.

Determine the test statistic.

Fx=

What is the p-value?

=

State the conclusion about the population means.

(Reject, Do not reject) H0. Conclude that there is(no, a)

significant difference between the means.

b. Was the blocking effective? Why or why not?

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

A.

H0:

Not all the 's are equal.

H1:

1=2==8

B.

H0:

All the 's are different.

H1:

1=2==8

C.

H0:

1=2==8

H1:

All the 's are different.

D.

H0:

1=2==8

H1:

Not all the 's are equal.

Determine the test statistic.

FBL=

What is the p-value? =

State the conclusion about the blocking.

(Reject, Do not reject) H0. There(is no, is) evidence suggesting that the blocking was effective.

c. If warranted, determine which pairs of balls were different using =0.05.

The driving distances for (balls A and B and balls A and C), (balls A and B and balls B and C), (balls A and C), (balls A and C and balls B and C),(balls A and B) were different.

8. The owner of a chain of three bagel shops would like to investigate if there is a difference in the number of bagels sold per day at each location. A random week was selected and the number of bagels sold each day at each location was recorded. The accompanying table shows the data. Complete parts a through c below.

Day	Store 1	Store2	Store 3
Monday	159	185	169
Tuesday	144	190	161
Wednesday	159	183	171
Thursday	149	167	158
Friday	141	188	145
Saturday	159	172	146
Sunday	160	175	163

a. Using =0.05, does there appear to be a difference in the number of bagels sold per day by the three stores? What are the correct hypotheses to test for differences between the stores?

A.

H0:

1=2=3

H1:

All the 's are different.

B.

H0:

1=2=3

H1:

Not all the 's are equal.

C.

H0:

Not all the 's are equal.

H1:

1=2=3

D.

H0:

All the 's are different.

H1:

1=2=3

Determine the test statistic.

Fx=

What is the p-value?

=

b. Was the blocking effective? Why or why not? What are the correct hypotheses to test for differences in the block means?

A.

H0:

All the 's are different.

H1:

Mon=Tues==Sun

B.

H0:

Mon=Tues==Sun

H1:

All the 's are different.

C.

H0:

Not all the 's are equal.

H1:

Mon=Tues==Sun

D.

H0:

Mon=Tues==Sun

H1:

Not all the 's are equal.

Determine the test statistic.

FBL=

What is the p-value?

=

State the conclusion about the blocking.

(Reject, Do not reject) H0. There (is, is no) evidence suggesting that the blocking was effective.

c. If warranted, determine which pairs of stores were different using

=0.05.

The number of bagels sold at

(Stores 1&2 and stores 3&4), (None), (Stores 1&3 and Stores 2&3), (stores 1&2, Stores 1&3, stores 2&3), (Stores 2&3)

were different.

9. Consider the accompanying data collected for a two-way ANOVA.

a)	Using =0.05, is there significant interaction between Factors A and B?
b)	Using =0.05, are the Factor A means different?
c)	Using =0.05, are the Factor B means different?

Factor A
Factor B	Level 1	Level 2	Level 3
Level 1	8	30	30
	19	21	32
	32	22	36
Level 2	22	22	35
	24	28	34
	14	20	22

a) Using = 0.05, is there significant interaction between Factors A and B? Identify the hypotheses for the interaction between Factors A and B. Choose the correct answer below.

A.

H0:

Factor A and B do interact,

H1:

Factor A and B do not interact

B.

H0:

AB,

H1:

A=B

C.

H0:

Factor A and B do not interact,

H1:

Factor A and B do interact

D.

H0:

A=B,

H1:

AB

Find the p-value for the interaction between Factors A and B.

=

Draw the appropriate conclusion for the interaction between Factors A and B. Choose the correct answer below.

A.

Reject the null hypothesis. There is sufficient evidence to conclude that Factors A and B interact.

B.

Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

C.

Donotreject the null hypothesis. There is insufficient evidence to conclude that Factors A and B interact.

D.

Donotreject the null hypothesis. There is insufficient evidence to conclude that the means differ.

b) Using = 0.05, are the Factor A means different?

Identify the hypotheses to test for Factor A. Choose the correct answer below.

A.

H0:

A1=A2=A3,

H1:

A1>A2>A3

B.

H0:

A1A2A3,

H1:

A1=A2=A3

C.

H0:

A1=A2=A3,

H1:

Not all Factor A means are equal

D.

H0:

A=B,

H1:

AB

Find the p-value for Factor A.

=

Draw the appropriate conclusion for Factor A. Choose the correct answer below.

A.

Donotreject the null hypothesis. There is sufficient evidence to conclude that the means differ.

B.

Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor A means are equal.

C.

Donotreject the null hypothesis. There is insufficient evidence to conclude that not all Factor A means are equal.

D.

It is inappropriate to draw a conclusion from this test because the Factors A and B interact.

c) Using = 0.05, are the Factor B means different? Identify the hypotheses to test for Factor B. Choose the correct answer below.

A.

H0:

A=B,

H1:

AB

B.

H0:

B1B2,

H1:

B1=B2

C.

H0:

B1=B2=B3,

H1:

Not all Factor B means are equal

D.

H0:

B1=B2,

H1:

Not all Factor B means are equal

Find the p-value for Factor B.

=

(Round to three decimal places as needed.)

Draw the appropriate conclusion for Factor B. Choose the correct answer below.

A.

Donotreject the null hypothesis. There is insufficient evidence to conclude that not all Factor B means are equal.

B.

Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor B means are equal.

C.

Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

D.

It is inappropriate to draw a conclusion from this test because the Factors A and B interact.

10. Consider the accompanying data collected for a two-way ANOVA.

a)	Using =0.05, is there significant interaction between Factors A and B?
b)	Using =0.05, are the Factor A means different?
c)	Using =0.05, are the Factor B means different?

Factor A
FactorB	Level 1	Level 2	Level 3
Level 1	8	9	11
	7	12	29
	15	20	23
Level 2	27	31	26
	9	20	36
	17	18	33
Level 3	40	40	39
	34	27	36
	24	39	31

a) Using = 0.05,is there significant interaction between Factors A and B? Identify the hypotheses for the interaction between Factors A and B. Choose the correct answer below.

A.

H0:

Factor A and B do not interact,

H1:

Factor A and B do interact

B.

H0:

Factor A and B do interact,

H1:

Factor A and B do not interact

C.

H0:

AB,

H1:

A=B

D.

H0:

A=B,

H1:

AB

Find the p-value for the interaction between Factors A and B.

=

(Round to three decimal places as needed.)

Draw the appropriate conclusion for the interaction between Factors A and B. Choose the correct answer below.

A.

Donotreject the null hypothesis. There is insufficient evidence to conclude that the means differ.

B.

Donotreject the null hypothesis. There is insufficient evidence to conclude that Factors A and B interact.

C.

Reject the null hypothesis. There is sufficient evidence to conclude that Factors A and B interact.

D.

Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

b) Using =0.05, are the Factor A means different? Identify the hypotheses to test for Factor A. Choose the correct answer below.

A.

H0:

A=B,

H1:

AB

B.

H0:

A1=A2=A3,

H1:

Not all Factor A means are equal

C.

H0:

A1A2A3,

H1:

A1=A2=A3

D.

H0:

A1=A2=A3,

H1:

A1>A2>A3

Find the p-value for Factor A.

=

(Round to three decimal places as needed.)

Draw the appropriate conclusion for Factor A. Choose the correct answer below.

A.

Donotreject the null hypothesis. There is sufficient evidence to conclude that the means differ.

B.

Donotreject the null hypothesis. There is insufficient evidence to conclude that not all Factor A means are equal.

C.

Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor A means are equal.

D.

It is inappropriate to draw a conclusion from this test because the Factors A and B interact.

c) Using =0.05, are the Factor B means different? Identify the hypotheses to test for Factor B. Choose the correct answer below.

A.

H0:

B1=B2=B3,

H1:

Not all Factor B means are equal

B.

H0:

A=B,

H1:

AB

C.

H0:

B1=B2,

H1:

Not all Factor B means are equal

D.

H0:

B1B2B3,

H1:

B1=B2=B3

Find the p-value for Factor B.

=

(Round to three decimal places as needed.)

Draw the appropriate conclusion for Factor B. Choose the correct answer below.

A.

Donotreject the null hypothesis. There is sufficient evidence to conclude that the means differ.

B.

Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor B means are equal.

C.

Donotreject the null hypothesis. There is insufficient evidence to conclude that not all Factor B means are equal.

D.

It is inappropriate to draw a conclusion from this test because the Factors A and B interact.