QNT 351 Entire Class
Assignments Problems and Discussion Questions – A Graded Work
QNT 351 Complete
Class Quantitative Analysis for Business Latest Version
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QNT 351 Week 1
Individual Statistics in Business
Write a
300-word summary that addresses the following criteria:
·
Define statistics.
·
Identify different types and levels of
statistics.
·
Describe the role of statistics in business
decision making.
Provide at
least three examples or problem situations in which statistics was used or
could be used.
QNT 351 Week 2
Learning Team Data Collection
Use either the data one of your Learning Team members retained from
RES/351 or the data from University of Phoenix Material: Ballard
Integrated Managed Services, Inc.,
Part 1.
Discuss with your team whether you have data
from RES/351, and if your team would like to use one team member’s data for the
Learning Team assignments in this course.
If
using data from RES/351:
Resources: Data collected from RES/351
Prepare a 700- to 1,050-word written report
along with a 5- to 7-slide Microsoft® PowerPoint®
presentation for the senior management team or stakeholders of your RES/351
research project to present your findings.
Address the following:
·
Present
the chosen situation as an overview—problem, purpose, research questions, and
hypotheses.
·
Describe
the instrument used for data collection.
·
Identify
types of data—quantitative, quantitative, or both—and how the data is
collected.
·
Identify
the level of measurement for each of the variables involved in the study.
·
Code
the data if you have not done so. Describe how the data is coded and evaluate
the procedure used.
·
Clean
the data by eliminating the data input errors made.
·
Draw
conclusions about appropriateness of the data to meet the purpose of the study.
If you
decide not to use your own data, you can use the Ballard Integrated
Managed Services, Inc., case
study overview:
Resources: University of Phoenix Material: Ballard
Integrated Managed Services, Inc.,
Part 1
Review the Ballard Integrated Managed
Services, Inc. (BIMS), Part 1
case study overview.
Prepare a 700- to 1,050-word written report
along with a 5- to 7-slide Microsoft® PowerPoint®
presentation for the senior management team to present your findings (see
Exhibit D for the data set of the second survey).
Address the following:
·
Present
the BIMS situation as an overview—problem, purpose, research questions, and
hypotheses.
·
Describe
the instrument used for data collection.
·
Identify
types of data collected—quantitative, qualitative, or both—and how the data is
collected.
·
Identify
the level of measurement for each of the variables involved in the study.
·
Code
the data if you have not done so. Describe how the data is coded and evaluate
the procedure used.
·
Clean
the data by eliminating the data input errors made.
·
Draw
conclusions about appropriateness of the data to meet the purpose of the study.
Note. As consultants to BIMS, your Learning
Team is expected to prepare and deliver a professional product addressing the
client's needs.
QNT
351 Week 3
Individual MyStatsLab Problems
Complete the assigned problems in
MyStatsLab available on the student website.
Learning Team
Summarizing and
Presenting Data
If
using RES/351 data:
Revise
the report submitted in Week Two based on the feedback provided by the
instructor in the Learning Team assignment, and insight gained by reading.
Summarize the data collected using descriptive
statistics. Descriptive statistics should be in the forms of frequency distribution
table, measures of mean, median, mode, standard deviation, and graphical
display of data.
Summarize the statistics in relation to the
problem selected and research questions and draw conclusions.
Prepare a 1,050- to 1,750-word report of conclusions
drawn from the data and make recommendations to the management.
Support recommendations by citing literature
consistent with APA guidelines.
If
using the Ballard Integrated Managed Services, Inc., (BIMS) case study overview:
Revise
the report submitted in Week Two based on the feedback provided by the
instructor in the Learning Team assignment, and insight gained by reading.
Analyze
the data included in BIMS case study Part 1 by computing descriptive statistics
in the form of tables, charts, measures of central tendency, and variability.
Prepare a
1,050- to 1,750-word report of conclusions drawn from the data and make
recommendations to the management.
Support recommendations by citing
literature consistent with APA guidelines.
QNT 351 Week 4
Individual
MyStatsLab
Problems
Complete the assigned problems in
MyStatsLab available on the student website.
Learning Team
Reflection
Discuss the
following with your Learning Team:
·
The steps in testing a research hypothesis
·
Comparing the means of two or more groups
·
Calculating the correlation between two
variables
Include
the topics you feel comfortable with, any topics you struggled with, and how
the weekly topics relate to application in your field.
Prepare a 350- to 1,050-word paper
detailing the findings of your discussion.
QNT 351 Week 5
Individual
MyStatsLab
Problems
Complete the assigned problems in
MyStatsLab available on the student website.
Learning Team
Analyzing and
Interpreting Data
If
using RES/351 data:
Ask your instructor for specific information regarding the analysis you
are required to perform for your data set.
Combine your Week Two Learning Team assignment
and Week Three findings with Week Five findings and make a recommendation to
the research problem.
Use the statistical tables given in the appendices of the textbook and a
statistical analysis application: a Microsoft® Excel®
spreadsheet, Minitab® statistical software, or SPSS™ software.
Prepare a 1,050- to 1,750-word written report
along with a 7- to 9-slide Microsoft® PowerPoint®
presentation for the senior management team to present your findings.
If
using the Ballard Integrated Managed Services, Inc. (BIMS) case study overview:
Resource: University of Phoenix
Material: Ballard Integrated Managed Services, Inc., Part 2.
Read the University of Phoenix Material: Ballard Integrated Managed
Services, Inc., Part 2. Your team acts as a consultant group that analyzes and
interprets this second set of data. The intent is to increase senior
management’s understanding of the sources of employee dissatisfaction and to
create a model that predicts employee resignation.
Combine your Week Two Learning Team assignment
and Week Three findings with Week Five findings and make a recommendation to
BIMS.
Use the statistical tables given in the appendices of the textbook and a
statistical analysis application: a Microsoft® Excel® spreadsheet,
Minitab® statistical software, or SPSS™ software.
Prepare a 1,050- to 1,750-word written report
along with a 7- to 9-slide Microsoft® PowerPoint®
presentation for the senior management team to present your findings (see
Exhibit D for the data set of the second survey).
Note. As consultants to BIMS, your Learning
Team is expected to prepare and deliver a professional product addressing the
client’s needs.
Discussion
Questions
QNT 351 Week 1 Discussion
Questions
How
would you define dependent and independent variables? What is their
significance in research? Explain with examples.
How
would you define a variable? What is the difference between a dependent and
independent variable? Do you think both variables are used in every research?
Explain why or why not. Provide examples.
What
is the importance of statistics in business decision making? Describe a
business situation where statistics was used in making a decision.
What
are the four data measurement scales? Provide two examples and explain the
importance of each in business research.
Where
would you see descriptive statistics used in your work place?
Develop five
demographic questions to measure gender, age, years of experience, level of
education, and ethnicity. Identify the level of measurement used for each
QNT 351 Week 2 Discussion
Questions
Can mean, median, or mode be calculated from all
statistical data? Explain why or why not. When is the mean the best measure of
central tendency? When is the median the best measure of central tendency?
Describe a business situation, other than what has
already been selected by fellow students or selected from the team assignment,
where mean and standard deviation can be used in decision making. Describe how
calculation of mean and standard deviation can help in making a decision.
What
level of data is a telephone number? Explain.
Does
all data have a mean, median, or mode? Why or why not? When is the mean the
best measure of central tendency? When is the median the best measure of
central tendency?
Why is the population shape a concern when
estimating a mean? What effect does sample size, n, have on the estimate of the
mean?
QNT 351 Week 3 Discussion
Questions
What are the differences between probability and
coincidence? Can the probability be more than 1 or less than 0? Explain why or
why not.
What
is the role of probability concepts in business decision-making? Provide
specific examples.
What
are the basic differences between a discrete and a continuous distribution?
What
are the characteristics of standard normal distribution? Explain how to
calculate the z-test static. Explain how a z-value is used to calculate the
area under the distribution and the meaning of P(0 to z) when z = 1.96.
QNT
351 Week 4 Discussion Questions
What are some terms related to hypothesis testing
with which you are already familiar? Why do null and alternative hypotheses
have to be mutually exclusive?
Why does the significance level differ among
industries? Will the null hypothesis be more likely to be rejected at α = 0.01
than α = 0.10? As the significance level increases to α = 0.10 from α = 0.01,
which type error is more likely to occur? What can be done to reduce the
likelihood of incurring this error?
Please
explain the five steps used in hypothesis testing. How does the five-step
procedure for hypothesis testing differ when comparing two groups using a t- or z-test? How is the process similar?
Please
explain terms related to hypothesis testing; please explain null and alternate
hypotheses, explain the difference between two different test statistics, then
define the equations used in both. Why
do null and alternative hypotheses have to be mutually exclusive?
Problems
Week 2 Problems
1.Choose
the correct answer bellow:
A.
It is an estimate or prediction or some other generalization about a population
based on information contained in a sample
B.
It is a characteristic or property of an individual experimental unit
C.
It is the process used to assign numbers to variables of individual population
units
D.
It is the science that deals with collection, classification, and
interpretation of information or data
2.
Explain the difference between qualitative and quantitative data
Choose
the correct answer bellow
A.
Quantitative data are collected from an observational study , while qualitative
data are from a designed experiment
B.
Quantitative data are data from a sample, while qualitative data are data from
a population
C.
Quantitative data are numerical in nature, while qualitative data are
categorical in nature
D.
Quantitative data are data from a population, while qualitative data are data
from a sample
E.
Quantitative data are categorical in nature, while qualitative data are
numerical in nature
F.
Quantitative data are collected from a designed experiment, while qualitative
data are from a observational study
3.
Explain how populations and variables differ. Choose the correct answer bellow:
A. A
population is a set of units of interest to a study. A variable is a subset of
the units of a population
B. A
variable is a set of units of interest to a study. A population is a
characteristic or property of the units being studied.
C. A
population is a set of units of interest to a study. A variable is an object
upon which data is collected
D. A
population is a set of units of interest to a study. A variable is a
characteristic or property of the units being studied
4.
Define statistical thinking. Choose the correct answer bellow:
A.
Statistical thinking involves applying rational thought and the science of
statistics to critically assess data and interferences
B.
Statistical thinking is a statement about the degree of uncertainty associated
with a statistical inference
C.
Statistical thinking utilizes sample data to make estimates, decisions,
predictions, or other generalization about a larger set of data
D.
Statistical thinking is a series of actions or operations that transforms
inputs to outputs
5.
Suppose you’re given a data set that classifies each sample unit into one of
four categories: A,B,C or D. You plan to create a computer database consisting
of these data, and you decide to code the data as A=, B=, C=3, and D=4. Are the
data consisting of the classifications A, B, C, and D qualitative or
quantitative? After the data are input as 1, 2, 3, or 4, are they qualitative
or quantitative?
Are
the data consisting of the classifications A, B, C, and D qualitative or
quantitative?
A.
Quantitative, because they are measured on a naturally occurring numerical sale
B.
Quantitative, because they can only be classified into categories
C.
Qualitative, because they can only be classified into categories
D.
Qualitative, because they are measured on a naturally occurring numerical sale
After
the data are input as 1, 2, 3, or 4, are they qualitative or quantitative?
A.
Qualitative, because they are measured on a naturally occurring numerical sale
B.
Quantitative, because they are measured on a naturally occurring numerical sale
C.
Qualitative, because they cannot be meaningfully added, subtracted, multiplied,
or divided
D.
Quantitative, because they cannot be meaningfully added, subtracted,
multiplied, or divided
6. A
company tracked all credit card purchases during the year 2005 and measured two
variables: (1) the cardholder’s town of residence, and (2) the amount (in
dollars) of each monthly payment
a.
identify the type (qualitative or quantitative) of each variable measured
b.
does the data set collected represent a population or a sample?
a.
Is the variable (1) qualitative or quantitative?
• Qualitative
• Quantitative
Is
the variable (2) qualitative or quantitative?
• Quantitative
• Qualitative
b.
Does the data set collected represent a population or a sample?
• Sample
• Population
7.
Identify each of the following variables as qualitative or quantitative
a.
college major
b.
distance of commute to work
c.
number of pets in a family
d.
natural hair color
a.
Is a college major qualitative or quantitative?
• Qualitative
• Quantitative
b.
Is distance of commute to work qualitative or quantitative?
• Qualitative
• Quantitative
c.
Is number of pets in a family qualitative or quantitative
• Qualitative
• Quantitative
d.
Is natural hair color qualitative or quantitative?
• Qualitative
• Quantitative
8.
Identify each of the following variables as qualitative or quantitative
a.
Eye color
b.
Number of brothers and sisters
c.
Size of home
d.
Political party preference
a.
Is the variable qualitative or quantitative? Why?
• Eye color is a quantitative variable.
Its values are not numerical
• Eye color is a qualitative variable.
Its values are not numerical
• Eye color is a qualitative variable.
Its values are numerical
• Eye color is a quantitative variable.
Its values are numerical
b.
Is the variable qualitative or quantitative? Why?
• Numbers of brothers and sisters is a
quantitative variable. Its values are not numerical
• Numbers of brothers and sisters is a
quantitative variable. Its values are numerical
• Numbers of brothers and sisters is a
qualitative variable. Its values not numerical
• Numbers of brothers and sisters is a
qualitative variable. Its values are not numerical
c.
Is the variable qualitative or quantitative? Why?
• Size of home is a quantitative
variable. Its values are not numerical
• Size of home is a qualitative
variable. Its values are not numerical
• Size of home is a qualitative
variable. Its values are numerical
• Size of home is a quantitative
variable. Its values are numerical
d.
Is the variable qualitative or quantitative? Why?
• Political party preference is
quantitative variable. Its values are not numerical
• Political party preference is
quantitative variable. Its values are numerical
• Political party preference is
qualitative variable. Its values not numerical
• Political party preference is
qualitative variable. Its values are not numerical
9. A
company surveyed a random sample of 10,000 employees in the region. One
question the asked was, “ If your employer provides you with mentoring
opportunities are you likely to remain in your job for the next five years?”
The found that 730 members of the sample said yes.
a.
Identify the population of interest in the company
• The 10,000 employees surveyed
• All people in the region
• The 730 employees who answered yes
• All employees in the region
b.
Based on the question posed by the company what is the variable of interest?
• If they answered yes to the survey
question
• If the employees are provided with
mentoring opportunities
• How long the employees are likely to
remain in their job
• The number of employees surveyed
c.
Is the variable quantitative or qualitative?
• The variable is a quantitative
variable. Its values can be expressed on a naturally occurring numerical scale
• The variable is a qualitative variable.
Its values cannot be expressed on a naturally occurring numerical scale
• The variable is a qualitative
variable. Its values can be expressed on a naturally occurring numerical scale
• The variable is a quantitative
variable. Its values cannot be expressed on a naturally occurring numerical
scale
d.
Describe the sample
• All people in the region
• The 10,000 employees surveyed
• All employees in the region
• The 730 employees who answered yes
10.
Identify each of the following variables as qualitative or quantitative
• Amount one paid on taxes
• Storage space on a computer drive
• Nationality
• Favorite baby name
a.
Is the variable qualitative or quantitative? Why?
• Amount one paid on taxes is a
quantitative variable. Its values are not numerical
• Amount one paid on taxes is a
quantitative variable. Its values are numerical
• Amount one paid on taxes is a
qualitative variable. Its values are not numerical
• Amount one paid on taxes is a
qualitative variable. Its values are numerical
b.
Is the variable qualitative or quantitative? Why?
• Storage space on a computer drive is a
qualitative variable. Its values are not numerical
• Storage space on a computer drive is a
quantitative variable. Its values are not numerical
• Storage space on a computer drive is a
qualitative variable. Its values are numerical
• Storage space on a computer drive is a
quantitative variable. Its values are numerical
c.
Is the variable qualitative or quantitative? Why?
• Nationality is a qualitative variable.
Its values are not numerical
• Nationality is a quantitative
variable. Its values are not numerical
• Nationality is a qualitative variable.
Its values are numerical
• Nationality is a quantitative
variable. Its values are numerical
d.
Is the variable qualitative or quantitative? Why?
• Favorite baby name is a qualitative
variable. Its values are numerical
• Favorite baby name is a qualitative
variable. Its values are not numerical
• Favorite baby name is a quantitative
variable. Its values are not numerical
• Favorite baby name is a quantitative
variable. Its values are numerical
Week 3 Problems
1.
An industrial group reports that there were approximately 122,000 industrial
robots operating in a region last year. The graph shows the percentages of
industrial robot units assigned to each of six task categories.
Complete
parts a through e bellow.
a. What type of graph is used to describe the data?
A. Pie chart
B. Bar graph
C. Pareto diagram
b. Identify the variable measured for each of the 122,000
industrial robots
A. Percentage of industrial robots
B. Number of industrial robots
C. Efficiency of each industrial robot
D. Task of each industrial robot
c. Use the graph to identify the task that uses the lowest
percentage of industrial robots
A. Arc welding
B. Assembly
C. Material handling
D. Material removal
E. Dispensing/coating
F. Spot welding
d. How many of the 122,000 industrial robots are used for
assembly?
6100 industrial robots
e. What percentage of industrial robots are used for either arc
welding or dispensing/coating?
43%
2. In one university, language professors incorporated a 10-week
extensive readings program to improve students’ Japanese reading comprehension.
The professor collected 262 books originally written for Japanese children and
required their students to read at least 40 of them as part of the grade in
course. The books were categorized into
reading levels (color-coded for easy selection) according to length and
complexity. Complete parts a trough c.
a. Compute the relative frequencies in each category.
Reading Level Relative
frequency
Level 1 (Red) .160
Level 2 (Blue) .279
Level 3 (Yellow) .195
Level 4 (Pink) .317
Level 5 (Orange) .038
Level 6 (Green) .011
b. Construct a relative frequency bar graph for the data. Choose the correct graph bellow
A. 
B. 
C.
B. C.
c. Convert the relative frequency bar graph into a Pareto diagram.
Interpret the graph. Choose the correct graph bellow
A. 
B. 
C. 
B. C.
Use the diagram to identify the reading level that occurs more often.
Choose the correct answer bellow
Level 4 Level 3
Level 2 Level 6
Level 1 Level 5
3. One organization estimates that there are 13,140 rhinoceroses
living in the wild in a continent. A breakdown of the number of rhinos of each
species is reported in the accompanying table. Complete parts a trough c.
a. One of the 13,140 rhinoceroses is selected and the species of
the rhinoceros is determined. What type of data (quantitative or qualitative)
is measured?
A. Qualitative
B. Quantitative
b. Construct a frequency bar chart for the data. Choose the
correct graph bellow.
A. 
B. 
C. 
D. 
B. C. D.
Correct answer D
c. Convert the frequency bar chart, part b, into a Pareto diagram.
Interpret the results
A. 
B. 
C. 
D. 
B. C. D.
Correct answer D
The most populated species of rhinoceros appear to be the African
White and the least most populated species seems to be the Javan
4. One organization estimates that there are 13,090 rhinoceroses
living in the wild in a continent. A breakdown of the number of rhinos of each
species is reported in the accompanying table. Complete parts a through c.
a. One of the 13,090 rhinoceroses is selected and the species of
the rhinoceroses is determined. What type of data (qualitative or quantitative)
is measured?
A. Quantitative
B. Qualitative
b. construct a frequency bar chart for the data. Choose the
correct graph bellow.
A. 
B
C. 
D. 
B C. D.
c. Convert the frequency bar chart, part b, into a Pareto diagram.
Interpret the results. Choose the correct graph bellow.
A. 
C. 
D. 
C. D.
Interpret the results
The most populated species of rhinoceros appear to be and the
least most populated species seems to be the
5. A government study found that the number of non-cash payments
in a country reached 92.7 billion transactions during the year 2007. The pie
chart to the right describes the proportions of these non-cash transactions
that were made with credit cards (CC), debit cards (D), checks (C), electronic
benefit transfers (EBT) cards, and automatic clearing house (ACH) payments.
Complete parts a trough d.
a. Describe the population of interest in the study. Choose the
correct answer bellow.
A. The population is the country making the transactions during
the year
B. The population is the government that conducted the survey
C. The population is all transactions made using a credit card or
debit card during the year
D. The population is all non-cash transactions made during the
year
b. Estimate the number of non-cash payments in 2007 that were made
with credit cards
21.32 billion
c. What percentage of all non-cash payments in 2007 were made with
either credit or debit cards?
49%
d. Convert the pie chart into a Pareto diagram and interpret the
figure. Choose the correct graph bellow
A. 
B. 
C. 
B. C.
Correct answer C
Interpret the figure. Choose the correct answer bellow.
A. The figure shows that EBT cards, ACH payments, and credit cards
have approximately the same percentage and that checks have almost no
representation.
B. The figure shows that the data are different when viewed in a
pie chart than in a Pareto diagram
C. The figure shows that checks, debit cards, and credit cards
have the largest percentages and that EBT cards have almost no representation
D. An interpretation cannot be made given the information of this
problem
6. A group of marketing professors asked every fourth adult
entrant to a mall to participate in a study. A total of 106 shoppers agreed to
answer the question, “Made locally’ means what percentage of local labor and
materials?” The responses of the 106 shoppers are summarized in the table to
the right. Complete parts a trough c bellow.
a. What type of data-collection method was used?
A. Designed experiment
B. Survey
C. Observational study
D. Published source
b. What type of variable, quantitative or qualitative, is
measured?
A. Qualitative
B. Quantitative
c. Present the data in the table in graphical form. Which bar
graph bellow correctly represents the data in the table?
A. 
B. 
B.
7. Use the relative frequency table shown to the right to
calculate the number of the 400 measurements falling into each of the
measurement classes. Then graph a frequency histogram for these data.
Calculate the number of measurements that fall
into each class
Choose the correct graph bellow
A. 
B. 
B.
C. 
8. Use the relative frequency table shown to the right to
calculate the number of the 400 measurements falling into each of the
measurement classes. Then graph a frequency histogram for these data.
Calculate the number of measurements that fall
into each class
Choose the correct graph bellow
A. 
B. 
B.
C. 
9. Consider the stem-and-leaf display to the right: 
a. How many observations were in the original
data set?
b. In the bottom row of the stem-and-leaf
display, identify the stem, and the numbers in the original data set
represented by this stem and its leaves.
c. Re-create all the numbers in the data set and
construct a dot plot
a. How many observations were in the original data set?
There were __ observations in the original data set
b. In the bottom row of the stem-and-leaf
display, identify the stem, and the numbers in the original data set
represented by this stem and its leaves.
A. The stem is 078 and the leaf is 0. The number
in the original data set is 10
B. The stem is 0 and the leaves are 0, 7, 8. The
numbers in the original data set are 10, 17, 18
C. The stem is 0 and the leaves are 0, 7, 8. The
numbers in the original data set are 0, 7, 8.
D. The stem is 078 and the leaf is 0. The number
in the original data set is 0
c. Re-create all the numbers in the data set and
construct a dot plot
A. 
B. 
B.
C. 
10. Certain measurements are summarized in the
histogram to the right. What percentage of the measurement are greater then 12?
The histogram shows that __ of the measurements
are greater than 12
11. Calculate the mean and median of the
following grade point averages.
2.1
3.8 2.7 3.4
2.3 3.3
Mean=
Median
12. Calculate the mean for samples for which the sample size and
∑x are given bellow
a. n=10, ∑x=83
b. n=16, ∑x=352
c. n=45, ∑x=36
d. n=18, ∑x=238
_
13. Five banks have been
ranked by the amount charged to credit and debit cards issued by the banks. The
table to the right gives the total amount charged in 2007 for the top ranked
banks.
a. Find the mean amount
charged for the top five banks and practically interpret this value
b.
Find the median amount charged for the top five banks and practically interpret
this value.
a. The mean amount
charged for the top five banks is billion
Interpret this value.
Choose the correct answer bellow
A. This value is the
amount that was charged most often by the top 5 banks.
B. This value is the
average amount charged by the top 5 banks
C. Approximately half of
the 5 charged amounts are greater than this value
b. The median amount
charged for the top five banks is $450.57 billion
Interpret this value.
Choose the correct answer bellow
A. Approximately half of
the 5 charged amounts are greater than this value
B. This value is the
amount that was charged most often by the top 5 banks
C. This value is the
average amount charged by the top 5 banks
14. Calculate the range,
variance, and standard deviation for the following sample
5,
2,1,0,1
Range
Sample variance
Sample standard deviation,
15. Calculate the variance and standard deviation for samples with
the following statistics
a. The variance is
The standard deviation
is
b. The variance is
The standard deviation
is
c. The variance is
The standard deviation
is
Week 4 Problems
1. Determine whether the random variable is discrete or
continuous.
a. the number of textbook authors now sitting at a computer
b. the weight of a T-bone steak
c. the number of fish caught during a fishing tournament
d. the time it takes to fly from city A to city B
e. the number of points scored during a basketball game
2. Determine whether the random variable is discrete or
continuous. In each case, state the possible values of the random variable.
(a) the number of light bulbs that burn out in the next week in
room with 17 bulbs
(b) the amount of rain in City B during April
(a) Is the number of light bulbs that burn out in the next week in
room with 17 bulbs discrete or continuous?
A. The random variable is continuous. The possible values are
0≤x≤17
C. The random variable is continuous. The possible values are 0,
1, 2, …,
D. The random variable is discrete. The possible values are 0≤x≤17
(b) Is the amount of rain in City B during April discrete or
continuous?
A. The random variable is discrete. The possible values are r=1,
2, 3, …
B. The random variable is discrete. The possible values are r≥0
D. The random variable is continuous. The possible values are r=1,
2, 3, …
3. The random variable x has the following discrete probability
distribution. Complete parts a trough f.
a. List the values x may assume.
b. What value of x is most probable?
c. Display the probability distribution as a graph. Choose the correct graph bellow.
A. 
B. 
B.
C. 
D. 
D.
d. Find P(x=8)
e. Find P(x≥5)
f. Find P(x>2)
4. A discrete random variable x can assume five possible values 2,
3, 5, 7, and 9. Its probability distribution is shown here. Complete parts a
trough c.
a. What is p(5)?
b. What is the probability that x equals 2 or 9?
c. What is p (x≤7)?
5. Toss three fair coins and let x equal the number of tails
observed.
a. Identify the sample points associated with this experiment and
assign a value of x to each sample point
b. Calculate p(x) for the values x=1 and x=2
c. Construct a graph for p(x)
d. What is P(x=2 or x=3)?
a. Choose the correct answer bellow
B. x=1, 2, 3
C. x=0, 1, 2
D. x=1, 2
b. Calculate p(x) for x=1
p(1) = .375
Calculate p(x) for x=2
p(2) = .375
c. Choose the correct graph bellow
A. 
B. 
B.
C. 
D. 
D.
6. Find the following probabilities for the standard normal random
variable z.
a. P(z>1.79) b. P(z<
-1.46) c. P(0.54 ≤ z ≤ 2.67) d. P(- 2.34 < z > 1.77)
7. Find the area under the standard normal probability
distribution between the following pairs of z – scores.
a. z=0 and z=3.00
b. z=0 and z=1.00
c. z=0 and z=2.00
d. z=0 and z=0.62
8. Find the area under the standard normal probability
distribution between the following pairs of z – scores.
a. z=0 and z=1.00
b. z=0 and z=2.00
c. z=0 and z=3.00
d. z=0 and z=0.62
9. Find the following probability for the standard normal random variable
z.
10. Suppose the random variable x is best described by a normal
distribution with µ = 26 and = 5. Find the z score that corresponds to each
of the following x – values.
11. Suppose x is a normal distributed random variable with µ = 11
and = 2. Find each of the following probabilities.
a. P(x≥14.5) b.
P(x≤9) c. P(12.56≤x≤16.12) d.
P(5.84≤x≤13.42)
a. P(x≥14.5) = .0401
b. P(x≤9)= .1587
c. P(12.56≤x≤16.12)
d. d. P(5.84≤x≤13.42)
12. The ages of a group of 50 women are approximately normally
distributed with a mean of 48 years and a standard deviation of 5 years. One
woman is randomly selected from the group, and her age is observed.
a. Find the probability that her age will fall between 55 and 59
years.
b. Find the probability that her age will fall between 47 and 53
years.
c. Find the probability that her age will be less than 35 years.
d. Find the probability that her age will exceed 41 years
13. Financial analysts who make forecasts of stock prices are
categorized as either “buy-side” analysts or “sell-side” analysts. The mean and
standard deviation of the forecast errors for both types of analysts are shown
is the table to the right. Assume that the distribution of forecast errors are
approximately normally distributed.
a. Find the probability that a buy-side analyst has a forecast
error of + 2.01 or higher
b. Find the probability that a sell-side analyst has a forecast
error of + 2.01 or higher
a. the probability that a buy-side analyst has a forecast error of
b. the probability that a sell-side analyst has a forecast error
of
14. The mean gas mileage for a hybrid car is 57 miles per gallon.
Suppose that the gasoline mileage is approximately normally distributed with a
standard deviation of 3.5 miles per gallon.
a. What is the probability that a randomly selected hybrid gets
more than 62 miles per gallon?
b. What is the probability that a randomly selected hybrid gets 50
miles per gallon or less?
c. What is the probability that a randomly selected hybrid gets
between 57 and 62 miles per gallon?
d. What is the probability that a randomly selected hybrid gets
less than 46 miles per gallon?
a. the probability that a randomly selected hybrid gets more than
62 miles per gallon is
b. the probability that a randomly selected hybrid gets 50 miles
per gallon or less is
c. the probability that a randomly selected hybrid gets between 57
and 62 miles per gallon
d. the probability that a randomly selected hybrid gets less than
46 miles per gallon
15. Resource Reservation Protocol (RSVP) was originally designed
to establish signaling links for stationary networks. RSVP was applied to mobile
wireless technology. A simulation study revealed that the transmission delay
(measured is milliseconds) of an RSVP linked wireless device has an approximate
normal distribution with mean µ=46.5 milliseconds and = 8.5 milliseconds.
Complete part a and b.
a. What is the probability that the transmission delay is less
than 57 milliseconds?
b. What is the probability that the transmission delay is between
40 and 60 milliseconds?
Week 5 Problems
1. Which hypothesis, the null or the alternative, is the
status-quo hypothesis?
Choose the correct answer bellow
A. null hypothesis
B. alternative hypothesis
2. What is the level of significance of a test of hypothesis?
Choose the correct answer bellow
A. The level of significance, β, is the probability of committing
a Type II error, rejecting the null hypothesis when it is, in fact, true
B. The level of
significance, α, is the probability of committing a Type II error, rejecting
the null hypothesis when it is, in fact, true
C. The level of significance, α, is the probability of committing
a Type I error, rejecting the null hypothesis when it is, in fact, true
D. The level of significance, β, is the probability of committing
a Type II error, not rejecting the null hypothesis when it is, in fact, false
E. The level of significance, β, is the probability of committing
a Type I error, rejecting the null hypothesis when it is, in fact, true
F. The level of significance, α, is the probability of committing
a Type I error, not rejecting the null hypothesis when it is, in fact, false
3. For each of the following rejection regions, sketch the
sampling distribution for z and indicate the location of the rejection region,
and determine the probability that a Type I error will be made.
a. z < - 1.645 b. z
> 2.575 c. z < - 1.28 or z >
1.28 d. z < - 2.33
Which sketch bellow shows the sampling distribution for the
rejection region z < - 1.645?
A. 
B. 
C. 
B. C.
What is the probability that a Type I error will be made for z
< - 1.645?
α=.05
b. Which sketch bellow shows the sampling distribution for the
rejection region z > 2.575?
A. 
B. 
C. 
B. C.
What is the probability that a Type I error will be made for z
> 2.575?
α=.005
c. Which sketch bellow shows the sampling distribution for the rejection
region z < - 1.28 or z > 1.28?
A. 
B. 
C. 
B. C.
What is the probability that a Type I error will be made for z
< - 1.28 or z > 1.28?
α=0.2
d. Which sketch bellow shows the sampling distribution for the
rejection region z < - 2.33?
A. 
B. 
C. 
B. C.
What is the probability that a Type I error will be made for z
< - 2.33?
α=.01
4. A survey found that 55% of college professors believe that
their online education courses are as good as or superior to courses that use
traditional face-to-face instruction.
a. Give the null hypothesis for testing the claim made by the
survey.
b. Give the rejection region for a two tailed test conducted at
α=0.10
a. What is the null hypothesis?
H0: p=.55
b. What is the rejection region? Select the correct choice bellow
and fill in any answer boxes to complete your choice.
B. z < - 1.645 or z >
1.645
5. A university economist conducted a study of elementary school
lunch menus. During the state-mandated testing period, school lunches averaged
881 calories. The economist claimed that after the testing period ended, the
average caloric content of the school lunches increased significantly. Set up
the null and alternative hypothesis to test the economist’s claim.
Choose the correct answer bellow
A. H0: µ=881, Ha: µ>881
B. H0: µ=881, Ha: µ≠881
C. H0: µ=881, Ha: µ<881
D. H0: µ≠881, Ha: µ>881
6. A random sample of 100 observations from a population with
standard deviation 65 yielded a sample mean of 111. Complete parts a trough c.
a. Test the null hypothesis that µ=100 against the alternative
hypothesis that µ>100, using α=0.05. Interpret the results of the test.
A. H0 is rejected
B. H0 is not rejected
Interpret the results of the test. Choose the correct
interpretation bellow
A. There is sufficient evidence to indicate the true population
mean is greater than 100 at α=0.05
B. There is sufficient evidence to indicate the true population
mean is smaller than 100 at α=0.05
C. There is sufficient evidence to indicate the true population
mean is not equal to 100 at α=0.05
b. Test the null hypothesis that µ=100 against the alternative
hypothesis that µ≠100, using α=0.05. Interpret the results of the test.
A. H0 is rejected
B. H0 is not rejected
Interpret the results of the test. Choose the correct
interpretation bellow.
A. There is insufficient evidence to indicate µ is smaller than
100 at α = 0.05
B. There is sufficient evidence to indicate µ is greater than 100
at α = 0.05
C. There is insufficient evidence to indicate µ is not equal to
100 at α = 0.05
c. Compare the results of the two tests you conducted. Explain why
the results differ. Choose the correct answer bellow.
A. The results differ because the alternative hypothesis in part a
is more specific than the one in b.
B. The results differ because the alternative hypothesis in part b
is more specific than the one in a.
C. The results do not differ because these two tests are
equivalent.
7. A study of n=59 hospital employees found that the number of
latex gloves used per week by the sampled workers is summarized by x = 23.1 and
s = 13.7. Let µ represent the mean number of latex gloves used per week by all
hospitals employees. Consider testing H0: µ=27 against Ha: µ<27.
a. Give the rejection region for the test at a significance level
of α=0.01
b. Calculate the value of the test statistic
c. Use the results, parts a and b, to make the appropriate
conclusion
a. What is the rejection region for the test? Choose the correct
answer bellow
A. z>2.575
B. z<-2.33
C. z<-2.33 or z>2.33
D. z<-2.575 or z>2.575
E. z>2.33
F. z<-2.575
b. What is the value of the test statistic?
c. What is the appropriate conclusion at a=0.01?
A. Do not reject H0. There is
sufficient evidence to indicate that µ<27
B. Reject H0. There is
sufficient evidence to indicate that µ<27
C. Reject H0. There is
insufficient evidence to indicate that µ<27
D. Do not reject H0. There is
insufficient evidence to indicate that µ<27
8. A satellite photograph of an urban area was divided into 4x4
meter areas (called pixels). Of interest is a numerical measurement of the
distribution of gaps or hole sizes in the pixel, called lacunarity. The mean
and standard deviation of the lucanarity measurements of 800 pixels randomly
selected from a specific urban area are 223 and 19, respectively. It is known
that the mean lacunarity measurements for all grassland pixels is 219. Do the
data suggest that the area sampled is grassland? Test at α=0.01
A. H0: µ0 = 219
Ha: µ0 > 219
B. H0: µ0 ≠ 219
Ha: µ0 = 219
C. H0: µ0 = 219
Ha: µ0 ≠ 219
D. H0: µ0 = 219
Ha: µ0 < 219
What is the rejection region for the test? Choose the correct
answer bellow.
A. z>2.575
B. z< - 2.33 or z>2.33
C. z< - 2.33
D. z>2.33
E. z< - 2.575
F. z< - 2.575 or z > 2.575
What is the value of the test statistic?
What is the appropriate conclusion at a=0.01?
A. Reject H0. There is
insufficient evidence to conclude that the area sampled is not grassland.
B. Do not reject H0. There is
insufficient evidence to conclude that the area sampled is not grassland.
C. Do not reject H0. There is
sufficient evidence to conclude that the area sampled is not grassland.
D. Reject H0. There is
sufficient evidence to conclude that the area sampled is not grassland.
9. In order to compare the means of two populations, independent
random sample of 390 observations are selected from each population, with the
results found in the table to the right. Complete parts a trough e.
a. Use a 95% confidence interval. Select the correct answer from
the options bellow.
A. We are 95% confident that the difference between the population
means falls in the confidence interval.
B. We are 95% confident that each of the population means falls
outside of the confidence interval.
C. We are 95% confident that each of the population means is
contained in the confidence interval.
D. We are 95% confident that the difference between the population
means falls outside of confidence interval
b. Test the null hypothesis H0:(µ1 - µ2) = 0 versus the
alternative hypothesis Ha: (µ1-µ2)≠0. Give the
significance level of the test, and interpret the result.
A. The p-value is approximately 0.0042, so we do not reject H0 for a > 0.0042
B. The p-value is approximately 0.0083, so we reject H0 for a > 0.0083
C. The p-value is approximately 0.0083, so we do not reject H0 for a > 0.0083
D. The p-value is approximately 0.0083, so we do not reject H0 for a > 0.0042
E. The p-value is approximately 0.0042, so we reject H0 for a > 0.0042
F. The p-value is approximately 0.0083, so we reject H0 for a > 0.0042
c. Suppose the test in part b was conducted with the alternative
hypothesis Ha:(µ1-µ2) > 0. How
would you answer to part b change?
A. The p-value would be 0.0042, so we would reject H0 for a >0.0042
B. The p-value would be 0.0042, so we would reject H0 for a >0.0083
C. The p-value would be 0.0083, so we would reject H0 for a >0.0083
D. The p-value would be 0.0083, but we would not reject H0 for a >0.0042
E. The p-value would be 0.0042, so we would not reject H0 for a >0.0042
F. The p-value would be 0.0083, but we would not reject H0 for a >0.0083
d. Test the null hypothesis H0: (µ1-µ2) = 22 versus Ha: (µ1-µ2)≠22. Give the significance level, and interpret the results.
A. The p-value is approximately 0.3790, so we do not reject H0 for a ≤ 0.1895
B. The p-value is approximately 0.1895, so we reject H0 for a ≤ 0.1895
C. The p-value is approximately 0.1895, so we reject H0 for a ≤ 0.3790
D. The p-value is approximately 0.1895, so we do not reject H0 for a ≤ 0.1895
E. The p-value is approximately 0.3790, so we reject H0 for a ≤ 0.3790
F. The p-value is approximately 0.3790, so we do not reject H0 for a ≤ 0.3790
e. What assumptions are necessary to ensure the validity of the
inferential procedures applied in parts a-d?
A. We must assume that the t-distribution should be used
B. We must assume that we have two small samples
C. We must assume that we have two independent random samples
D. We must assume that we have two dependent random samples
10. To use the t-statistic to test for a difference between the
means of two populations, what assumptions must be made about the two
populations? About the two samples?
What assumption must be made about the two populations? Select all
that apply.
A. Both sampled populations must be approximately normally
distributed.
B. Both sampled populations must have approximately equal
population variances
C. There must be more than 30 samples selected from each
population
D. Both populations must be selected independently for each other
What assumption must be made about the two samples? Select all
that apply.
A. The samples must be independent of each other
B. The samples must be normally distributed
C. There must be more than 30 samples selected from each
population
12. A survey was conducted to determine the impact of
contamination on property values. Home owners were randomly selected from each
of seven states – A, B, C, D, E, F and G. Each homeowner was asked to estimate
the property value of a home located in an area contaminated by a certain
substance. The dependent variable of interest was the substance discount
percentage ( the difference between the current home value and the estimated
value after contamination , as a percentage ). The researchers were interested
in comparing the mean substance discount percentages across the seven states.
Complete parts a and b.
a. Give the null and alternative hypotheses of interest to the
researchers. Choose the correct answer bellow.
A. H0: At least two
treatment means are equal
Ha: µ1 ≠ µ2 ≠ µ3 ≠ µ4 ≠ µ5 ≠ µ6 ≠ µ7
B. H0: At least two
treatment means differ
Ha: µ1 = µ2 = µ3 = µ4 = µ5 = µ6 = µ7
C. H0: µ1 = µ2 = µ3 = µ4 = µ5 = µ6 = µ7
Ha: At least two treatment means differ
D. H0: µ1 ≠ µ2 ≠ µ3 ≠ µ4 ≠ µ5 ≠ µ6 ≠ µ7
Ha: At least two treatment means are equal
b. An ANOVA summary table is shown to the right. Use the
information provided to conduct the hypothesis test, part a. Use a = 0.10
What is the rejection region? Select the correct choice bellow and
fill in the answer boxes to complete your choice.
Identify the test statistic, F.
F = 1.59
Identify the p-value
p = .166
Determine the conclusion for the hypothesis test. Choose the
correct answer bellow.
A. Fail to reject the null hypothesis. There is insufficient
evidence to conclude that at least two of the states differ with respect to the
mean substance discount percentages.
B. Reject the null hypothesis. There is insufficient evidence to
conclude that at least two of the states are equal with respect to the mean
substance discount percentages.
C. Reject the null hypothesis. There is sufficient evidence to
conclude that at least two of the states differ with respect to the mean
substance discount percentages.
D. Fail to reject the null hypothesis. There is sufficient evidence
to conclude that at least two of the states are equal with respect to the mean
substance discount percentages.
14. Explain what each of the following sample correlation
coefficients tells you about the relationship between the x and y values in the
sample.
a. r=1 b. r=-1 c. r=0
d. r=0.9 e. r=0.08 f. r= -0.97
a. What relationship exists between the x and y values in the
sample?
A. x and y have a weak, positive linear relationship
B. x and y have a strong, positive linear relationship
C. x and y have a weak, negative linear relationship
D. x and y have a perfect, negative linear relationship
E. x and y have a strong, negative linear relationship
F. x and y have a perfect, positive linear relationship
G. x and y are not linearly related
b. What relationship exists between the x and y values in the
sample?
A. x and y have a perfect, negative linear relationship
B. x and y have a strong, positive linear relationship
C. x and y have a perfect, positive linear relationship
D. x and y have a weak, negative linear relationship
E. x and y have a weak, positive linear relationship
F. x and y have a strong, negative linear relationship
G. x and y are not linearly related
c. What relationship exists between the x and y values in the
sample?
A. x and y have a weak, positive linear relationship
B. x and y have a perfect, positive linear relationship
C. x and y have a strong, positive linear relationship
D. x and y have a weak, negative linear relationship
E. x and y have a strong, negative linear relationship
F. x and y have a perfect, negative linear relationship
G. x and y are not linearly related
d. What relationship exists between the x and y values in the
sample?
A. x and y have a perfect, positive linear relationship
B. x and y have a strong, positive linear relationship
C. x and y have a strong, negative linear relationship
D. x and y have a weak, negative linear relationship
E. x and y have a weak, positive linear relationship
F. x and y have a perfect, negative linear relationship
G. x and y are not linearly related
e. What relationship exists between the x and y values in the
sample?
A. x and y have a weak, positive linear relationship
B. x and y have a weak, negative linear relationship
C. x and y have a strong, positive linear relationship
D. x and y have a strong, negative linear relationship
E. x and y have a perfect, positive linear relationship
F. x and y have a perfect, negative linear relationship
G. x and y are not linearly related
f. What relationship exists between the x and y values in the
sample?
A. x and y have a strong, positive linear relationship
B. x and y have a weak, positive linear relationship
C. x and y have a perfect, negative linear relationship
D. x and y have a perfect, positive linear relationship
E. x and y have a strong, negative linear relationship
F. x and y have a weak, negative linear relationship
G. x and y are not linearly related
QNT/351 Complete Class Week 1-5
QNT351 Full Class All Weeks 1,2,3,4,5
QNT 351
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