BUSA 208 – Business Stats Homework

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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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