Introduction to Probability and Statistics, 14th Edition by William Mendenhall – Test Bank
To Purchase this Complete Test Bank with Answers Click the link Below
If face any problem or
Further information contact us At tbzuiqe@gmail.com
Sample Test
MBB.IntroProb13.ch03sec1-4
TRUE/FALSE
1. If
the correlation coefficient , then all the data points lie exactly on a straight
line.
ANS:
T
PTS: 1
2. The
correlation coefficient r is
a number that indicates the direction and the strength of the relationship
between the dependent variable y and
the independent variable x.
ANS: T
PTS: 1
3. If
the correlation coefficient , then there is no linear relationship whatsoever
between the dependent variable y and
the independent variable x.
ANS:
T
PTS: 1
4. A
perfect straight line sloping upward would produce a covariance value of +1.
ANS:
T
PTS: 1
5. A
perfect straight line sloping downward would produce a covariance value of –1.
ANS:
T
PTS: 1
6. The
standard deviation is a measure of the linear relationship between two
quantitative variables.
ANS:
F
PTS: 1
7. Generally
speaking, if two quantitative variables are unrelated, the covariance will be a
positive or negative number close to zero.
ANS:
T
PTS: 1
8. The
best fitting line relating the dependent variable y to the
independent variable x,
often called the regression or least-squares line, is found by minimizing the
sum of the squared differences between the data points and the line itself.
ANS:
T
PTS: 1
9. The
scatterplot is a graph that is used to graphically represent the relationship
between two quantitative variables.
ANS:
T
PTS: 1
10.
When constructing a scatterplot, the independent variable (x) is placed on the
horizontal axis, and the dependent variable (y)
is placed on the vertical axis.
ANS:
T
PTS: 1
11.
A scatterplot is not particularly useful in determining if the
relationship between the independent and dependent variables is not linear.
ANS:
F
PTS: 1
12.
If the linear relationship between the dependent and independent
variables is positive, the scatterplot will show the data points on the (x, y) plane generally
moving from the lower left corner to the upper right corner.
ANS:
T
PTS: 1
13.
If the correlation coefficient between the independent variable x and the
dependent variable y is
0.87, then the best fitting line would have a slope equal to 0.87.
ANS: F
PTS: 1
14.
If two variables have a correlation coefficient equal to 0.005,
this means that there is no relationship between the two variables.
ANS:
F
PTS: 1
15.
A perfect correlation between two variables will always produce
a correlation coefficient of +1.0.
ANS:
F
PTS: 1
MULTIPLE CHOICE
1. Which
of the following are measures of the linear relationship between two variables?
|
a. |
the covariance |
|
b. |
the correlation coefficient |
|
c. |
the variance |
|
d. |
both the covariance and the correlation
coefficient |
|
e. |
both the correlation coefficient and
the variance |
ANS:
D
PTS: 1
2. Generally
speaking, if two variables are unrelated (as one increases, the other shows no pattern),
the covariance will be:
|
a. |
a large positive number |
|
b. |
a large negative number |
|
c. |
a positive or negative number close to
zero |
|
d. |
a positive or negative number close to
100 |
|
e. |
none of these |
ANS:
C
PTS: 1
3. Given
the least squares regression line y =
3.8 – 2x,
|
a. |
the relationship between x and y is positive |
|
b. |
the relationship between x and y is negative |
|
c. |
there is no linear relationship
between x and y |
|
d. |
as x decreases, so does y |
|
e. |
as x increases, so does y |
ANS:
B
PTS: 1
4. Given
that = 400, = 625, = 350, and n = 10, the
correlation coefficient is:
|
a. |
0.70 |
|
b. |
0.56 |
|
c. |
0.875 |
|
d. |
0.156 |
|
e. |
0.141 |
ANS:
A
PTS: 1
5. If a regression
line has a y-intercept
of 6.75 and a slope of 1.25, then when x =
2 the actual value of y is:
|
a. |
9.25 |
|
b. |
8.75 |
|
c. |
2.25 |
|
d. |
1.45 |
|
e. |
unknown |
ANS:
E
PTS: 1
6. A
perfect straight line sloping downward would produce a correlation coefficient
equal to:
|
a. |
+1 |
|
b. |
–1 |
|
c. |
+2 |
|
d. |
–2 |
|
e. |
0 |
ANS:
B
PTS: 1
7. If
all the points in a scatterplot lie on the least squares regression line, then
the correlation coefficient r must
be:
|
a. |
1.0 |
|
b. |
–1.0 |
|
c. |
either 1.0 or –1.0 |
|
d. |
100 |
|
e. |
10 |
ANS:
C
PTS: 1
8. A
manager of a supermarket wishes to show the relationship between the number of
customers who come to the store on weekends, and the total volume of sales (in dollars)
during the same weekend. Which of the following graphs would likely be most
useful if the manager has a sample of 52 weekends worth of data?
|
a. |
bar chart |
|
b. |
pie chart |
|
c. |
box and whisker plot |
|
d. |
scatterplot |
|
e. |
histogram |
ANS: D
PTS: 1
9. Given
that = 100, = 64, = 60, and n = 8, the slope of the best-fitting
regression line is:
|
a. |
0.75 |
|
b. |
0.64 |
|
c. |
0.60 |
|
d. |
7.5 |
|
e. |
6.4 |
ANS:
C
PTS: 1
10.
The best-fitting regression line can be used to:
|
a. |
find the actual value of y for a given
value of x |
|
b. |
estimate or predict the value of y for a given
value of x |
|
c. |
calculate the correlation coefficient |
|
d. |
all of these |
|
e. |
none of these |
ANS:
B
PTS: 1
11.
Which value of the correlation coefficient r indicates a
stronger correlation than 0.72?
|
a. |
0.65 |
|
b. |
–0.75 |
|
c. |
0.60 |
|
d. |
–0.70 |
|
e. |
0.55 |
ANS:
B
PTS: 1
12.
A scatterplot can be used to determine the relationship between:
|
a. |
two qualitative variables |
|
b. |
two quantitative variables |
|
c. |
one qualitative variable and one
quantitative variable |
|
d. |
all of these |
|
e. |
none of these |
ANS:
B
PTS: 1
13.
In constructing a scatterplot, it would not be appropriate to:
|
a. |
label the x axis |
|
b. |
label the y axis |
|
c. |
label the graph using titles |
|
d. |
connect the data points on the graphs
with straight lines |
|
e. |
draw the best fitting line on the graph |
ANS:
D
PTS: 1
PROBLEM
1. A councilman
was interested in determining whether people between the ages of 18 and 30
years of age will react to a piece of legislation differently than people over
30 years of age. The legislator polled a sample of 150 people from his
district. The resulting data is shown in the table below:
Construct a side-by-side bar chart.
Construct a pie chart for the 18 – 30 age group.
Construct a pie chart for the Over 30 age group.
Which of the two types of presentations in parts (a) and (b) is more
easily understood?
______________
ANS:
;
;
;
Pie chart
PTS: 1
2. Male
and female respondents to a questionnaire about gender differences are
categorized into three groups according to their answers as shown below:
Create a side-by-side bar chart to describe these data.
Create two pie charts (one for men and one for women) to
describe these data.
Men:
Women:
Which of the charts created above best depicts the difference or
similarity of the responses of men and women.
______________
ANS:
;
;
;
Pie charts
PTS: 1
3. A law
school administrator was interested in whether a student’s score on the
entrance exam can be used to predict a student’s grade point average (GPA)
after one year of law school. The administrator took a random sample of 15
students and computed the following summary information, where x = entrance exam
score and y =
GPA after one year:
and
Find the correlation between the entrance exam score and the
grade point average after one year of law school.
______________
Interpret the correlation coefficient found in part (a).
____________________________
Find the best fitting line relating grade point average after on
year of law school and score on the entrance exam.
y = ______________
If a student scored 91 on the entrance exam, what would you
predict the student’s grade point average to be after one year of law school?
______________
ANS:
0.934; There is a positive relationship; -1.6575 + 0.0568x;
3.5113
PTS: 1
4. When
the price of gasoline gets high, consumers become very concerned about the gas
mileage obtained by their cars. One consumer was interested in the relationship
between car engine size (number of cylinders) and gas mileage (miles/gallon).
The consumer took a random sample of 7 cars and recorded the following
information:
and
Would you expect the correlation between engine size and gas
mileage to be positive or negative?
______________
Find the correlation between engine size and gas mileage.
______________
Find the best fitting line relating car engine size and gas
mileage.
y = ______________
What would you predict the gas mileage to be for a car with
6-cylinder engine size?
______________ mpg
ANS:
Negative; -0.731; 34.405 – 2.5844x; 18.899
PTS: 1
5. The
manager of a movie rental store was interested in examining the relationship
between the weekly take-home pay for a family and the amount that family spends
weekly on recreational activities. The following output was generated using
Minitab:
Covariances
Let x =
weekly take-home pay, and y =
amount spent weekly on recreational activities.
1. Identify
the covariance between x and y.
______________
1. Identify
the variance of weekly take-home pay.
______________
1. Identify
the variance of amount spent weekly on recreational activities.
______________
1. Calculate
the correlation between weekly take-home pay and amount spent weekly on
recreational activities.
______________
1. Interpret
the correlation coefficient found in part (d).
____________________________
ANS:
2419.64; 4413.84; 1364.29; 0.986; There is a positive
relationship
PTS: 1
6. A
soft drink distributor was interested in examining the relationship between the
number of ads (x)
for his product during prime time on a local television station and the number
of sales per week (y)
in thousands of cases. He compiled the figures for 20 weeks and computed the
following summary information:
and
Find the correlation coefficient for the number of ads during
prime time and weekly sales.
______________
Find the best-fitting line relating the number of ads during
prime time and weekly sales.
y = ______________
If the soft drink distributor ran 21 TV ads per week for his
product, what would you predict his sales to be?
______________ thousand cases
ANS:
0.908; 0.1256 + 1.8966x; 39.9542
PTS: 1
7. The
number of household members, x and
the amount spent on groceries per week, y (rounded
to the nearest dollar) are measured for eight households in the Big Rapids
area. The data are shown below:
Create a raw scatterplot of these eight data points (no
regression line or equation).
Find the best-fitting regression line for these data.
y = ______________
Plot the points and the best-fitting line on the same graph.
What would you estimate a household of seven to spend on
groceries per week?
______________
Should you use the fitted line to estimate this amount?
______________
Why or why not?
________________________________________________________
ANS:
;
0.1681 + 25.546x;
;
178.99; No; It is risky to try to estimate the value of y for a
value of x outside the experimental region – that is, the range of x values for
which you have collected data.
PTS: 1
MBB.IntroProb13.ch04sec5-6
TRUE/FALSE
1. The
intersection of events A and B is the event
that A or B or both occur.
ANS:
F
PTS: 1
2. The
complement of an event A,
denoted by , consists of all the simple events in the sample space S that are not in A.
ANS:
T
PTS: 1
3. The
conditional probability of event B,
given that event A has
occurred is defined by: .
ANS:
T
PTS: 1
4. Two
events A and B are said to be
independent if and only if P(A / B) = P(B) or P(B / A) = P(A).
ANS:
F
PTS: 1
5. If P(A) > 0, P(B) > 0, and P(A B) = 0, then the
events A and B are
independent.
ANS:
F
PTS: 1
6. If P(A) = 0.4, P(B) = 0.5, and P(A B) = 0.20,
then the events A and B are
mutually exclusive.
ANS:
F
PTS: 1
7. If P(A) > 0 and P(B) > 0, then
when A and B are mutually
exclusive events, they are also dependent events.
ANS: T
PTS: 1
8. If P(A) = 0.3, P(A B) = 0.7, and P(A B) = 0.2, then P(B) = 0.2.
ANS:
F
PTS: 1
9. If P(A) = 0.4, P(B) = 0.5, and P(A B) = 0.7, then P(A B) = 0.2.
ANS:
T
PTS: 1
10.
If P(A) = 0.60, P(B) = 0.40, and P(B / A) = 0.60, then P(A / B) = 0.24.
ANS:
F
PTS: 1
11.
If A and B are
independent events with P(A) = 0.30 and P(B) = 0.50, then P(A/B) is 0.15.
ANS:
F
PTS: 1
12.
The probability that event A will not occur is 1- .
ANS:
F
PTS: 1
13.
If P(A / B) = P(A), then events A and B are said to
be independent.
ANS:
T
PTS: 1
14.
Conditional probability is the probability that an event will
occur, with no other events taken into consideration.
ANS:
F
PTS: 1
15.
If A and B are two
independent events with P(A) = 0.25 and P(B) = 0.45, then P(A B) = 0.70.
ANS:
F
PTS: 1
16.
If P(A) = 0, P(B) = 0.4, and P(A B) = 0, then
events A and B are independent.
ANS:
T
PTS: 1
17.
Two events A and B are said to be
independent if P(A B) = P(A) + P(B).
ANS:
F
PTS: 1
18.
Two events A and B are said to
mutually exclusive if P(A B) = 0.
ANS:
T
PTS: 1
19.
Suppose A and B are mutually
exclusive events where P(A) = 0.1 and P(B) = 0.7, then P(A B) = 0.8.
ANS:
F
PTS: 1
20.
Suppose A and B are mutually
exclusive events where P(A) = 0.2 and P(B) = 0.3. Then P(A B) = 0.5.
ANS:
T
PTS: 1
21.
Suppose A and B are events
where P(A) = 0.4, P(B) = 0.5, and P(A B) = 0.2. Then P(B / A) = 0.4.
ANS:
F
PTS: 1
22.
All the outcomes contained in one or the other of two events (or
possibly in both) constitute the union of two events.
ANS:
T
PTS: 1
23.
The additive rule of probability is used to compute the
probability for an intersection of two or more events: namely, given two
events A and B, and also
ANS:
F
PTS: 1
24.
The addition law of probability theory is used to compute the
probability for the occurrence of a union of two or more events; namely, given
two events A and B,
ANS:
T
PTS: 1
MULTIPLE CHOICE
1. Which
one of the following is always true for two events, A and B?
|
a. |
If A and B are
independent, they are also mutually exclusive. |
|
b. |
If A and B are dependent,
they are also mutually exclusive. |
|
c. |
If P(A
/ B) = P(A B), A and B are independent. |
|
d. |
If A and B are mutually
exclusive, then A B can never occur on the same trial of an experiment. |
|
e. |
All of these. |
ANS:
D
PTS: 1
2. is:
|
a. |
the union of two events |
|
b. |
the intersection of two events |
|
c. |
the complement of an event |
|
d. |
the additive rule of probability |
|
e. |
none of these |
ANS:
C
PTS: 1
3. The
probability of an event and the probability of its complement always sum to:
|
a. |
–1 |
|
b. |
0 |
|
c. |
1 |
|
d. |
any value between 0 and 1 |
|
e. |
0.5 |
ANS:
C
PTS: 1
4. Suppose P(A) = 0.4, P(B) = 0.3, and P(A B) = 0. Which one of the
following statements correctly defines the relationship between events A and B?
|
a. |
Events A and B are
independent, but not mutually exclusive. |
|
b. |
Events A and B are mutually
exclusive, but not independent. |
|
c. |
Events A and B are
neither mutually exclusive nor independent. |
|
d. |
Events A and B are both
mutually exclusive and independent. |
|
e. |
None of these. |
ANS: B
PTS: 1
5. If
events A and B are
mutually exclusive, then the probability of both events occurring
simultaneously is equal to:
|
a. |
–1 |
|
b. |
0 |
|
c. |
1 |
|
d. |
any value between 0 and 1 |
|
e. |
0.5 |
ANS: B
PTS: 1
6. If P(A/B) = P(A), or P(B/A) = P(B), then events A and B are said to
be:
|
a. |
mutually exclusive |
|
b. |
disjoint |
|
c. |
independent |
|
d. |
dependent |
|
e. |
B contains A. |
ANS:
C
PTS: 1
7. If P(A) = 0.80, P(B) = 0.70 and P(A B) = 0.90, then P(A B) is:
|
a. |
0.60 |
|
b. |
0.56 |
|
c. |
0.72 |
|
d. |
0.63 |
|
e. |
0.5 |
ANS:
A
PTS: 1
8. If P(A) = 0.30, P(B) = 0.40 and P(A B) = 0.20, then P(A / B) is:
|
a. |
0.12 |
|
b. |
0.08 |
|
c. |
0.67 |
|
d. |
0.50 |
|
e. |
0.3 |
ANS: D
PTS: 1
9. If P(A) = 0.40, P(B) = 0.30 and P(A B) = 0.12,
then A and B are:
|
a. |
dependent events |
|
b. |
independent events |
|
c. |
mutually exclusive events |
|
d. |
disjoint events |
|
e. |
none of these |
ANS: B
PTS: 1
10.
If P(A) = 0.42 and P(B) = 0.38, then P(A B) is:
|
a. |
0.80 |
|
b. |
0.58 |
|
c. |
0.04 |
|
d. |
0.42 |
|
e. |
Cannot be determined from the given
information. |
ANS:
E
PTS: 1
11.
All the outcomes (simple events) contained in one or the other
of two random events, or possibly in both, make up:
|
a. |
the events of an experiment |
|
b. |
the intersection of two events |
|
c. |
the probability space of an experiment |
|
d. |
the union of two events |
|
e. |
the complement of the other event |
ANS:
D
PTS: 1
12.
Which of the following clearly describes the general
multiplicative rule of probability?
|
a. |
It is a rule of probability theory that
is used to compute the probability for the occurrence of a union of two or
more events: for any two events, A and B, . |
|
b. |
It is a rule of probability theory that
is used to compute the probability for the occurrence of a union of two or
more events: for any two events A and B, . |
|
c. |
It is a rule of probability theory that
is used to compute the probability for an intersection of two or more events:
for any two events, A and B, |
|
d. |
It is a rule of probability theory that
is used to compute the probability for an intersection of two or more events:
for any two events A and B, |
|
e. |
All of these. |
ANS:
C
PTS: 1
13.
Which of the following best describes the concept of marginal
probability?
|
a. |
It is a measure of the likelihood that
a particular event will occur, regardless of whether another event occurs. |
|
b. |
It is a measure of the likelihood that
a particular event will occur, given the fact that another event has already
occurred or is certain to occur. |
|
c. |
It is a measure of the likelihood of
the simultaneous occurrence of two or more events. |
|
d. |
It is a direct way for defining the
sample space of an experiment. |
|
e. |
It is a measure of the likelihood that
a particular event will not occur. |
ANS:
A
PTS: 1
14.
In the case of independent events A, B, and C, equals:
|
a. |
|
|
b. |
|
|
c. |
|
|
d. |
|
|
e. |
ANS:
C
PTS: 1
15.
Two events A and B are said to
be dependent if and only if:
|
a. |
P(A)
= P(B) |
|
b. |
P(A)
increases along with P(B) |
|
c. |
P(A)
increases as P(B) decreases |
|
d. |
event A is
affected or changed by the occurrence of event B |
|
e. |
P(A)
< P(B) |
ANS:
D
PTS: 1
PROBLEM
1. A
group of forty people at a health club were classified according to their
gender and smoking habits, as shown below:
Round your answers to four decimal places, if necessary.
1. One
person is selected at random from that group of forty people. What is the
probability the person smokes?
______________
1. What
is the probability the person is female but does not smoke?
______________
1. What
is the probability the person is male?
Comments
Post a Comment