# BUSA 208 Chapter 121 Business Stats Homework Assignment

Question

Exam

Name___________________________________

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 Sum Average Variance

1 3 2473.08 824.36 740.996

2 3 2411.911 803.9705 1120.791

3 3 2495.924 831.9748 2958.509

4 3 2494.92 831.64 489.802

5 3 2487.995 829.3318 1129.897

6 3 2351.078 783.6925 443.6333

7 3 2319.392 773.1308 4450.131

8 3 2373.183 791.0609 468.4032

9 3 2350.24 783.4132 2173.944

10 3 2416.553 805.5178 1200.471

11 3 2479.895 826.6317 905.5771

12 3 2393.605 797.8684 382.9982

13 3 2245.545 748.515 11513.88

14 3 2361.247 787.0824 1364.083

15 3 2418.24 806.08 1147.566

16 3 2379.708 793.2361 3115.073

17 3 2494.709 831.5696 3092.78

18 3 2389.693 796.5643 5503.197

19 3 2358.984 786.3279 6874.581

20 3 2273.107 757.7023 15.62739

US 20 15708.57 785.4287 1867.925

Germany 20 16453.12 822.6558 1841.004

Japan 20 15807.32 790.366 2408.399

ANOVA

Source of Variation SS df MS F P-value F crit

Rows 34378.73 19 1809.407 0.840232 0.649989 1.867331

Columns 16352.4 2 8176.198 3.796773 0.031385 3.244821

Error 81831.48 38 2153.46

Total 132562.6 59

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)

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:

x1 = 62.1 x2 = 58.94 x3 = 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.

2)

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:

x1 = 62.1 x2 = 58.94 x3 = 71.2

SST = 6016

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.

3)

2

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.

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

4)

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

and standard transmissions (factor A?Sample) 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:

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

5)

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.

6)

3

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.

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.

7)

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.

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

Fertilizer A 300 400 200 500 400

Fertilizer B 150 200 100 150 200

Fertilizer C 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.

8)

4

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 Model B Model C

37 43 28

33 39 32

36 35 33

38 38

40

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.

9)

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:

x1 = 62.1 x2 = 58.94 x3 = 71.2

SST = 6016

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.

10)

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. D) reject H0.

11)

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

C) The frequencies computed from H0

D) The frequencies found in the population being examined

12)

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

A) The frequencies computed from H0

B) The frequencies found in the sample being examined

C) The frequencies found in the population being examined

D) the frequencies computed from H1

13)

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.

Regularly use text

messaging

Do not regularly

use text messaging

Under 21 82 38

21-39 57 34

40 and over 6 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.

14)

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.

Regularly use text

messaging

Do not regularly

use text messaging

Under 21 82 38

21-39 57 34

40 and over 6 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

15)

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

C) Not all population means are equal. D) Ho

: ?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)

6

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

20)

7

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