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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A major consumer group recently undertook a study to determine whether automobile customers

would rate the quality of cars differently that were manufactured in the U.S., Europe, or Japan. To

conduct this test, a sample of 20 individuals was asked to look at mid- range model cars made in

each of the three countries. The individuals in the sample were then asked to provide a rating for

each car on a scale of 1 to 1000. The following computer output resulted, and the tests were

conducted using a significance level equal to 0.05.

Anova: Two- Factor Without Replication

SUMMARY

Count

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

Sum

2473.08

2411.911

2495.924

2494.92

2487.995

2351.078

2319.392

2373.183

2350.24

2416.553

2479.895

2393.605

2245.545

2361.247

2418.24

2379.708

2494.709

2389.693

2358.984

2273.107

Average

824.36

803.9705

831.9748

831.64

829.3318

783.6925

773.1308

791.0609

783.4132

805.5178

826.6317

797.8684

748.515

787.0824

806.08

793.2361

831.5696

796.5643

786.3279

757.7023

Variance

740.996

1120.791

2958.509

489.802

1129.897

443.6333

4450.131

468.4032

2173.944

1200.471

905.5771

382.9982

11513.88

1364.083

1147.566

3115.073

3092.78

5503.197

6874.581

15.62739

20

20

20

15708.57

16453.12

15807.32

785.4287

822.6558

790.366

1867.925

1841.004

2408.399

ANOVA

Source of Variation

Rows

Columns

Error

SS

34378.73

16352.4

81831.48

df

19

2

38

Total

132562.6

59

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

US

Germany

Japan

MS

1809.407

8176.198

2153.46

F

0.840232

3.796773

Based upon the data, which of the following statements is true?

A) The primary null hypothesis should not be rejected.

B) Blocking was effective.

C) The averages for the 20 people are not all the same.

D) Blocking was not effective.

1

P- value

0.649989

0.031385

F crit

1.867331

3.244821

1)

2) The State Transportation Department is thinking of changing its speed limit signs. It is considering

two new options in addition to the existing sign design. At question is whether the three sign

designs will produce the same mean speed. To test this, the department has conducted a limited

test in which a stretch of roadway was selected. With the original signs up, a random sample of 30

cars was selected and the speeds were measured. Then, on different days, the two new designs

were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the

following summary statistics were computed based on the data:

x 1 = 62.1

x 2 = 58.94

2)

x 3 = 71.2

The appropriate test to conduct to determine if the population means are equal is:

A) one- way analysis of variance

B) three sample t- test.

C) Hartley’s F- max test.

D) randomized complete block analysis of variance.

3) The State Transportation Department is thinking of changing its speed limit signs. It is considering

two new options in addition to the existing sign design. At question is whether the three sign

designs will produce the same mean speed. To test this, the department has conducted a limited

test in which a stretch of roadway was selected. With the original signs up, a random sample of 30

cars was selected and the speeds were measured. Then, on different days, the two new designs

were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the

following summary statistics were computed based on the data:

x 1 = 62.1

SST = 6016

x 2 = 58.94

x 3 = 71.2

Based on these sample results and significance level equal to 0.05, the sum of squares between is:

A) approximately 1,215.

B) approximately 2,430.

C) approximately 3,586.

D) None of the above.

2

3)

4) A two- factor analysis of variance is conducted to test the effect that price and advertising have on

sales of a particular brand of bottled water. Each week a combination of particular levels of price

and advertising are used and the sales amount is recorded. The computer results are shown below.

4)

Based on the results above and a 0.05 level of significance, which of the following is correct?

A) There is no interaction between price and advertising, and both factors significantly affect

sales

B) There is interaction between price and advertising, so the above results conclusively show

that both factors affect price

C) There is no interaction between price and advertising, so results for individual factors may be

misleading

D) There is interaction between price and advertising, so the above results for individual factors

may be misleading

5) A national car rental company recently conducted a study recently in which cars with automatic

and standard transmissions (factor ASample) were rented to male and female customers (factor B

Columns). Three customers in each category were randomly selected and the miles driven per

day was recorded as follows:

5)

Based on the design of this study, how many degrees of freedom will be associated with the mean

square for factor A?

A) 2

B) 3

C) 8

D) 1

6) In a randomized complete block design analysis of variance, how many factors are there to be

analyzed?

A) Depends on the sample size in each treatment

B) Two factors

C) One factor, but multiple levels

D) Can’t be determined without additional information.

3

6)

7) A test is conducted to compare three difference income tax software packages to determine

whether there is any difference in the average time it takes to prepare income tax returns using the

three different software packages. Ten different people’s income tax returns are done by each of the

three software packages and the time is recorded for each. The computer results are shown below.

7)

Assuming that the hypothesis tests are conducted using a significance level equal to 0.05, the

Fisher’s LSD value for multiple comparisons is:

A) about 0.91.

B) approximately 1.91.

C) approximately 0.4985.

D) about 0.5387.

8) A large orchard owner in the state of Washington is interested in determining whether the mean

number of bushels of peaches per acre is the same or different depending on the type of tree that is

used. He also thinks that production may be affected by the type of fertilizer that is used. To test, he

has set up a test in which a one- acre plot of peach trees with a combination each of 5 varieties and 3

fertilizer types are studied. The following data reflect the number of bushels of peaches on each

acre plot.

Fertilizer A

Fertilizer B

Fertilizer C

Tree Type 1 Tree Type 2 Tree Type 3 Tree Type 4 Tree Type 5

300

400

200

500

400

150

200

100

150

200

300

300

400

200

500

Assuming that the hypothesis tests will be conducted using an alpha equal 0.05 level, which of the

following is true?

A) Based on the data, the grower can conclude that there is a difference in mean production of

peaches across the different types of tree.

B) The grower was justified in controlling for the fertilizer type since the test shows that blocking

was effective.

C) The total sum of squares is approximately 4,570,900.

D) A, B and C are all true.

4

8)

9) To test the mileage efficiency of three new car models, random samples of various sample sizes

were selected from each of the three cars and the mpg data obtained are shown below.

Model A

37

33

36

38

Model B

43

39

35

38

40

9)

Model C

28

32

33

Based on the sample date, one can conclude that

A) at least two car models have different mpgs.

B) Model C has a higher mpg than Model A.

C) all three car models have the same mean mpg.

D) None of the above.

10) The State Transportation Department is thinking of changing its speed limit signs. It is considering

two new options in addition to the existing sign design. At question is whether the three sign

designs will produce the same mean speed. To test this, the department has conducted a limited

test in which a stretch of roadway was selected. With the original signs up, a random sample of 30

cars was selected and the speeds were measured. Then, on different days, the two new designs were

installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the

following summary statistics were computed based on the data:

x 1 = 62.1

SST = 6016

x 2 = 58.94

10)

x 3 = 71.2

Based on these sample results and a significance level equal to 0.05, assuming that the null

hypothesis of equal means has been rejected, the Tukey- Kramer critical range is:

A) 1.96.

B) approximately 4.0.

C) Can’t be determined without more information.

D) None of the above.

11) Consider a goodness- of- fit test with a computed value of chi- square = 1.273 and a critical value =

13.388, the appropriate conclusion would be to:

A) take a smaller sample.

B) take a larger sample.

C) fail to reject H0 .

11)

D) reject H0 .

12) What does the term observed cell frequencies refer to?

A) The frequencies found in the sample being examined

B) The frequencies computed from H1

12)

C) The frequencies computed from H0

D) The frequencies found in the population being examined

13) What does the term expected cell frequencies refer to?

A) The frequencies computed from H0

13)

B) The frequencies found in the sample being examined

C) The frequencies found in the population being examined

D) the frequencies computed from H1

5

14) A cell phone company wants to determine if the use of text messaging is independent of age. The

following data has been collected from a random sample of customers.

Under 21

21 – 39

40 and over

Regularly use text

messaging

82

57

6

14)

Do not regularly

use text messaging

38

34

83

To conduct a contingency analysis using a 0.01 level of significance, the value of the critical value

is:

A) 11.0705.

B) 9.2104.

C) 15.0863.

D) 5.9915.

15) A cell phone company wants to determine if the use of text messaging is independent of age. The

following data has been collected from a random sample of customers.

Under 21

21 – 39

40 and over

Regularly use text

messaging

82

57

6

15)

Do not regularly

use text messaging

38

34

83

Based on the data above what is the expected value for the "under 21 and regularly use text

messaging" cell?

A) 120

B) 82

C) 58

D) 50

16) Which of the following is NOT one of the assumptions required by the randomized block design?

A) The populations have equal means.

B) The observations within samples are independent.

C) The populations are normally distributed.

D) The data measurement must be interval or ratio level.

16)

17) A hotel chain has four hotels in Oregon. The general manager is interested in determining whether

the mean length of stay is the same or different for the four hotels. She selects a random sample of n

= 20 guests at each hotel and determines the number of nights they stayed. Assuming that she plans

to test this using an alpha level equal to 0.05, which of the following is the appropriate alternative

hypothesis?

A) Ho: 1 = 2 = 3 = 4

B) 1 = 2 = 3 = 4

17)

18) How can the degrees of freedom be found in a contingency table with cross- classified data?

A) When df are equal to rows minus columns

B) Total number of cell minus 1

C) When df are equal to rows minus 1 multiplied by columns minus 1

D) When df are equal to rows multiplied by columns

18)

19) Which of the following is an assumption for the one- way analysis of variance experimental design?

A) The populations have equal variances.

B) All populations are normally distributed.

C) The observations are independent.

D) All of the above.

19)

D) Ho: 1 2 3 4

C) Not all population means are equal.

20) When testing for independence in a contingency table with 3 rows and 4 columns, there are

________ degrees of freedom.

A) 7

B) 6

C) 12

D) 5

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