Download Practice Test 2 –Bus 2023 Directions: For each question find the

Practice Test 2 –Bus 2023
Directions: For each question find the answer that is the best solution provided. There is only one
correct answer.
1.
Statistical studies in which researchers do not control variables of interest are
a.
b.
c.
d.
ANSWER:
experimental studies
uncontrolled experimental studies
not of any value
observational studies
d
2.
Statistical studies in which researchers control variables of interest are
a.
experimental studies
b.
control observational studies
c.
non experimental studies
d.
observational studies
ANSWER: a
3.
A portion of the population selected to represent the population is called
a.
statistical inference
b.
descriptive statistics
c.
a census
d.
a sample
ANSWER: d
4.
In a sample of 800 students in a university, 160, or 20%, are Business majors. Based on
the above information, the school's paper reported that "20% of all the students at the
university are Business majors." This report is an example of
a.
a sample
b.
a population
c.
statistical inference
d.
descriptive statistics
ANSWER: c
5.
Six hundred residents of a city are polled to obtain information on voting intentions in an
upcoming city election. The six hundred residents in this study is an example of a(n)
a.
census
b.
sample
c.
observation
d.
population
ANSWER: b
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6.
Since a sample is a subset of the population, a percentage that is calculated from the
sample data
a.
is always smaller than the corresponding percentage from the population
b.
is always larger than the corresponding percentage from the population
c.
must be equal to the corresponding percentage from the population
d.
can be larger, smaller, or equal to the corresponding percentage from the
population
ANSWER:
d
7.
A tabular method that can be used to summarize the data on two variables simultaneously
is called
a.
simultaneous equations
b.
a crosstabulation
c.
a histogram
d.
a dot plot
ANSWER: b
Exhibit 2-4
A survey of 400 college seniors resulted in the following crosstabulation regarding their
undergraduate major and whether or not they plan to go to graduate school.
Undergraduate Major
Graduate School
Business
Engineering
Others
Total
Yes
35
42
63
140
No
91
104
65
260
Total
126
146
128
400
8.
Refer to Exhibit 2-4. What percentage of the students does not plan to go to graduate
school?
a.
b.
c.
d.
ANSWER:
280
520
65
32
c
9.
Refer to Exhibit 2-4. What percentage of the students' undergraduate major is
engineering?
a.
b.
c.
d.
ANSWER:
292
520
65
36.5
d
2
10.
Refer to Exhibit 2-4. Of those students who are majoring in business, what percentage
plans to go to graduate school?
a.
27.78
b.
8.75
c.
70
d.
72.22
ANSWER:
a
11.
Refer to Exhibit 2-4. Among the students who plan to go to graduate school, what
percentage indicated "Other" majors?
a.
b.
c.
d.
ANSWER:
15.75
45
54
35
b
12.
The purpose of statistical inference is to provide information about the
a.
sample based upon information contained in the population
b.
population based upon information contained in the sample
c.
population based upon information contained in the population
d.
mean of the sample based upon the mean of the population
ANSWER: b
13.
A simple random sample of size n from a finite population of size N is a sample selected
such that each possible sample of size
a.
N has the same probability of being selected
b.
n has a probability of 0.5 of being selected
c.
n has a probability of 0.1 of being selected
d.
n has the same probability of being selected
ANSWER: d
14.
A simple random sample from an infinite population is a sample selected such that
a.
each element selected comes from the same population
b.
each element is selected independently
c.
each element selected comes from the same population and each element is
selected independently
d.
the probability of being selected changes
ANSWER: c
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15.
Stratified random sampling is a method of selecting a sample in which
a.
the sample is first divided into groups, and then random samples are taken from
each group
b.
various strata are selected from the sample
c.
the population is first divided into groups, and then random samples are drawn
from each group
d.
None of the alternative ANSWERS is correct.
ANSWER: c
16.
Cluster sampling is
a.
a nonprobability sampling method
b.
the same as convenience sampling
c.
a probability sampling method
d.
None of the alternative ANSWERS is correct.
ANSWER: c
17.
Convenience sampling is an example of
a.
probabilistic sampling
b.
stratified sampling
c.
a nonprobability sampling technique
d.
cluster sampling
ANSWER: c
18.
Which of the following is an example of a nonprobability sampling technique?
a.
simple random sampling
b.
stratified random sampling
c.
cluster sampling
d.
judgment sampling
ANSWER: d
19.
The range of probability is
a.
any value larger than zero
b.
any value between minus infinity to plus infinity
c.
zero to one
d.
any value between -1 to 1
ANSWER: c
20.
Any process that generates well-defined outcomes is
a.
an event
b.
an experiment
c.
a sample point
d.
None of the other answers is correct.
ANSWER: b
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21.
In statistical experiments, each time the experiment is repeated
a.
the same outcome must occur
b.
the same outcome can not occur again
c.
a different outcome may occur
d.
None of the other answers is correct.
ANSWER: c
22.
The collection of all possible sample points in an experiment is
a.
the sample space
b.
a sample point
c.
an experiment
d.
the population
ANSWER: a
23.
An experiment consists of tossing 4 coins successively. The number of sample points in
this experiment is
a.
16
b.
8
c.
4
d.
2
ANSWER: a
24.
A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9.
One chip is selected at random from each urn. The total number of sample points in the sample
space is
a.
30
b.
100
c.
729
d.
1,000
ANSWER: d
25.
Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many
possible selections are there?
a.
20
b.
7
c.
5!
d.
10
ANSWER: d
26.
The “Top Three” at a racetrack consists of picking the correct order of the first three
horses in a race. If there are 10 horses in a particular race, how many “Top Three” outcomes are
there?
a.
302,400
b.
720
c.
1,814,400
d.
10
5
ANSWER:
b
27.
The probability assigned to each experimental outcome must be
a.
any value larger than zero
b.
smaller than zero
c.
one
d.
between zero and one
ANSWER: d
28.
An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4.
The probability of outcome E4 is
a.
0.500
b.
0.024
c.
0.100
d.
0.900
ANSWER: c
29.
Given that event E has a probability of 0.25, the probability of the complement of event E
a.
cannot be determined with the above information
b.
can have any value between zero and one
c.
must be 0.75
d.
is 0.25
ANSWER: c
Recall that P(A) = 1-P(Ac). So we get 0.25 = 1 - P(Ac)  P(Ac) = 0.75
The symbol  shows the
a.
union of events
b.
intersection of events
c.
sum of the probabilities of events
d.
sample space
ANSWER: a
30.
31.
The union of events A and B is the event containing
a.
all the sample points common to both A and B
b.
all the sample points belonging to A or B
c.
all the sample points belonging to A or B or both
d.
all the sample points belonging to A or B, but not both
ANSWER: c
If P(A) = 0.38, P(B) = 0.83, and P(A  B) = 0.57; then P(A  B) =
a.
1.21
b.
0.64
c.
0.78
d.
1.78
ANSWER: b
Recall that P(A  B) = P(A)+P(B)- P(A  B) = 0.38+ 0.83 -0.57 = 0.64
32.
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If P(A) = 0.62, P(B) = 0.47, and P(A  B) = 0.88; then P(A  B) =
a.
0.2914
b.
1.9700
c.
0.6700
d.
0.2100
ANSWER: d
Recall that P(A  B) = P(A)+P(B)- P(A  B) = 0.62+0.47-0.88 = 0.21
33.
If P(A) = 0.85, P(A  B) = 0.72, and P(A  B) = 0.66, then P(B) =
a.
0.15
b.
0.53
c.
0.28
d.
0.15
ANSWER: b
Solve this the same as above…but for B
34.
35.
Two events are mutually exclusive if
a.
the probability of their intersection is 1
b.
they have no sample points in common
c.
the probability of their intersection is 0.5
d.
the probability of their intersection is 1 and they have no sample points in
common
36.
The multiplication law is potentially helpful when we are interested in computing the
probability of
a.
mutually exclusive events
b.
the intersection of two events
c.
the union of two events
d.
None of the other answers is correct.
ANSWER: b
If P(A) = 0.80, P(B) = 0.65, and P(A  B) = 0.78, then P(BA) =
a.
0.6700
b.
0.8375
c.
0.9750
d.
Not enough information is given to answer this question.
ANSWER: b
Recall P(BA) = P(A  B) / P(A) = 0.67 / 0.80 = 0.8375
37.
38.
If two events are independent, then
a.
they must be mutually exclusive
b.
the sum of their probabilities must be equal to one
c.
the probability of their intersection must be zero
d.
None of the other answers is correct.
ANSWER: d
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39.
If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A|B) =
a.
0.209
b.
0.000
c.
0.550
d.
None of the other answers is correct.
ANSWER: d
Recall that if A and B are independent that P(A|B) = P(A) = 0.38
40.
If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X|Y) =
a.
0.0944
b.
0.6150
c.
1.0000
d.
0.0000
ANSWER: d
Recall that if the events are mutually exclusive that P(X  Y) = 0
So we find that P(X|Y) = P(X  Y) / P(Y) = 0 / 0.32 = 0
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Short Answer: Answer all of the following questions. Make sure to show all work. Solutions
with no work will receive no credit.
1. The SAT math scores of a sample of business school students and their genders are shown
below.
SAT Math Scores
Gender
Less than 400
400 up to 600
600 and more
Total
Female
24
168
48
240
Male
40
96
24
160
Total
64
264
72
400
a.
How many students scored less than 400?
b.
How many students were female?
c.
Of the male students, how many scored 600 or more?
d.
Compute row percentages and comment on any relationship that may exist between SAT
math scores and gender of the individuals.
e.
Compute column percentages.
ANSWERS:
a.
64 – This is simply the column total for less than 64
b.
240 – This is simply the row total for female
c.
24 – So now we only look at the row for males and see how many scored greater than
600.
d. To do this we only divide each rows values by their respective row total.
SAT Math Scores
Gender
Less than 400
400 up to 600
Female
24/240 = 10% 168/240=70% 48/240=20%
100%
Male
40/160=25%
100%
96/160=60%
600 and more
24/160=15%
Total
From the above percentages it can be noted that the largest percentages of both genders' SAT
scores are in the 400 to 600 range. However, 70% of females and only 60% of males have SAT
scores in this range. Also it can be noted that 10% of females' SAT scores are under 400,
whereas, 25% of males' SAT scores fall in this category.
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e. Do the same thing but for columns
SAT Math Scores
Gender
Less than 400
400 up to 600
600 and more
Female
37.5%
63.6%
66.7%
Male
62.5%
36.4%
33.3%
Total
100%
100%
100%
If we look at the scores this way we can see that females were 2:1 when scoring 600 or more
and almost that same ratio for 400-600.
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2. A market research firm has conducted a study to determine consumer preference for a new
package design for a particular product. The consumers, ages were also noted.
Package Design
Age
A
B
C
Total
Under 25
18
18
29
65
25 – 40
18
12
5
35
Total
36
30
34
100
a.
b.
c.
d.
Which package design was most preferred overall?
What percent of those participating in the study preferred package A?
What percent of those under 25 years of age preferred package A?
What percent of those aged 25 - 40 preferred package A?
e.
Is the preference for package A the same for both age groups?
ANSWERS:
a.
Design A because it had the highest number of purchases.
b.
36 out of a 100 total or 36%
c.
So now we only look at the under 25 row and we find that it was (18/65)*100=27.7%
d.
Do the same thing, but for 25-40 or (18/35)*100=51.4%
e.
No, although both groups have the 18 people who prefer Design A, the percentage of
those in the “Under 25” age group who prefer Design A is smaller than that of the “25 –
40” age group (27.7% vs. 51.4%).
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3.
All the employees of ABC Company are assigned ID numbers. The ID number consists
of the first letter of an employee’s last name, followed by four numbers.
a.
How many possible different ID numbers are there?
b.
How many possible different ID numbers are there for employees whose last
name starts with an “A”?
ANSWERS:
a.
So we simply use the counting rule here. We have 5 spaces with 26 possible
outcomes for the first one (A-Z) and 10 numbers (0-9) for the last four. So we
get:
n1*n2*n3*n4*n5 = 26*10*10*10*10 = 26 * 104 = 260,000
b.
We can use the same rule, but now there is only one possible outcome for n1 and
we see that our expression becomes 1*n2*n3*n4*n5 = 1*10*10*10*10 = 1 * 104
= 10,000
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4.
The sales records of a real estate agency show the following sales over the past 200 days:
Number of
Number
Houses Sold of Days
a.
b.
c.
d.
e.
f.
0
60
1
80
2
40
3
16
4
4
How many sample points are there?
Assign probabilities to the sample points and show their values.
What is the probability that the agency will not sell any houses in a given day?
What is the probability of selling at least 2 houses?
What is the probability of selling 1 or 2 houses?
What is the probability of selling less than 3 houses?
ANSWERS:
a.
5 for the total number of possible houses sold { 0,1,2,3,4 }
b.
Number of
Houses Sold Probability
c.
d.
e.
f.
0
0.30
1
0.40
2
0.20
3
0.08
4
0.02
This is P(0) = 0.3
This is all the values greater than and including 2 = P (X ≥ 2)
= P(2) + P(3) + P(4) = 0.20 + 0.08+ 0.02 = 0.3
This is the probability of P(1) + P(2) = 0.4+ 0.2 =0.6
The probability of selling less than three houses is the same as 1- P(X≥3) by the
complement rule. This is easier to calculate = 1-P(3) + P(4) = 1 – 0.08 – 0.02 =
0.9
You can also add up the first directly P(0) + P(1) + P(2) = 0.90
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5. Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B) =
0.4.
a.
Find P(A  B).
b.
Find P(A  B).
c.
Find P(AB).
ANSWERS:
a.
If the events are mutually exclusive by definition the intersection does not exist so
P(A  B) = 0
b.
P(A  B) = P(A) + P(B) = 0.40 + 0.20 = 0.6
c.
P(AB) = P(A  B) / (B) = 0 / 0.40 = 0
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6. You are given the following information on Events A, B, C, and D.
P(A) = .4
P(B) = .2
P(C) = .1
a.
b.
c.
d.
e.
f.
g.
h.
P(A  D) = .6
P(AB) = .3
P(A  C) = .04
P(A  D) = .03
Compute P(D).
Compute P(A  B).
Compute P(AC).
Compute the probability of the complement of C.
Are A and B mutually exclusive? Explain your answer.
Are A and B independent? Explain your answer.
Are A and C mutually exclusive? Explain your answer.
Are A and C independent? Explain your answer.
ANSWERS:
a.
Recall that P(A  D) = P(A) + P(D) - P(A  D)
 P(D) = P(A  D) - P(A) + P(A  D) = 0.60 – 0.40 + 0.03 = 0.23
b.
Recall that P(AB) = P(A  B) / P (B)  P(A  B) = P(AB)*P(B)
0.30*0.20 = 0.06
c.
P(AC) = P(A  C) / P (C) = 0.04 / 0.10 = 0.4
d.
P(Cc) = 1 – P(C) = 1 – 0.10 = 0.9
e.
No, P(AB)  0. Since this is the case we know that P(A  B)  0. So since the
intersection is not equal to 0, A and B cannot be mutually exclusive.
f.
No, P(AB)  P(A) which is what is required for independence.
g.
No, P(A  C)  0
h.
Yes, P(AC) = P(A). Both are equal to 0.40 which means that event C does not
influence the outcome of event A. This is what it means to be independent.
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