Findings, Conclusions, & Recommendations
Report Writing
Findings
Conclusions
Recommendations
Findings
Conclusions
Recommendations
Findings
Data
Conclusions
What the data means
Recommendations
What should we do?
Types of Reports
Proposal
Feasibility
Analysis
Annual/Quarterly
Sales/Revenue
Investment
Marketing
Research
Consumer
Research
Types of Reports
Proposal
Feasibility
Analysis
Annual/Quarterly
Sales/Revenue
Investment
Marketing
Research
Consumer
Research
Report Sections
1. Title page
2. Table of contents
3. Executive summary
4. Body sections
a. Purpose
b. Scope
c. Factors
d. Conclusions
5. References (endnotes)
Report Sections
1. Title page
2. Table of contents
3. Executive summary
4. Body sections
a. Purpose
b. Scope
c. Factors
d. Conclusions
5. References (endnotes)
New Page
New Page
New Page
New Page
New Page
Title Page
1. Title
2. Author
3. Date (use due date)
4. Audience*
5. No page number
Findings
Conclusions
Recommendations
65% of employees use Facebook
during company time.
Employees are wasting time at
work.
We should establish a social
media policy.
Findings
Conclusions
Recommendations
SHA applications are down 15%.
Exploring Report Myths
Myth Truth
Reports are entirely different
from memos and letters.
Reports may be formatted as
memos or letters.
Exploring Report Myths
Myth Truth
Reports are strictly “objective”
presentations of factual data.
Report writers use their best
judgement to select data to
provide in reports.
Exploring Report Myths
Myth Truth
Reports are mere collections
of data: they should not
incorporate the writer’s
opinion.
Reports should be adapted to
the needs of the readers.
-If readers merely need numerical or
factual data, then mere numerical or
factual data should be sufficient.
Exploring Report Myths
Myth Truth
Reports are mere collections
of data: they should not
incorporate the writer’s
opinion.
Reports should be adapted to
the needs of the readers.
-If readers rely on the report writer to
interpret the data, then the report
should incorporate the writer’s best
attempt to draw conclusions and, if
appropriate, recommendations.
Exploring Report Myths
Myth Truth
A report should be structured
as a sequence of steps in
which the writer engaged in
the “discovery process” to
collect the data.
A report should be structured
according to the needs of the
readers: to learn conclusions
or to act on recommendations.
Google Report
Hilton Annual Report
Hilton Annual Report
Aramark
Report Examples
https://storage.googleapis.com/gfw-touched-accounts-
pdfs/google-cloud-security-and-compliance-whitepaper.pdf
http://ir.hilton.com/~/media/Files/H/Hilton-Worldwide-IR-
V3/annual-report/Hilton_2013_AR.pdf
http://ir.hilton.com/~/media/Files/H/Hilton-Worldwide-IR-
V3/annual-report/1948-Annual-Report.pdf
http://www.elon.edu/docs/e-
web/bft/sustainability/ARAMARK%20Trayless%20Dining%20J
uly%202008%20FINAL.pdf
MATH 245
1) 82.4%<p<84.6%
2) 0.164<p<0.266. Based on answering incorrectly
The procedure for constructing a confidence interval estimate
for a population proportion can
be found on page 1 of the Lesson 22 notes.
Make sure the number of "successes" and the number of
observations are entered into the
correct fields, and that the confidence level is correct.
Also, double check that your answers are entered as decimals
rounded to three places (add
trailing zeros as needed).
3) The lower confidence limit of restaurant B interval is greater
than the upper confidence
limit of restaurant A interval. Therefore, Restaurant B has a
significantly higher
proportion of inaccurate orders.
Restaurant B's lower limit lies within Restaurant A's interval.
Since the intervals
overlap, we cannot say Restaurant B has a significantly higher
proportion of inaccurate
orders.
4) 1)752
2)722
MTH 245 Lesson 22 Notes
One-Sample Interval Estimate of ��
The best estimator of a population proportion �� is the sample
proportion �̂��.
The true sampling distribution of �̂�� is binomial, but if ��
⋅ �̂�� ≥ 5 and
�� ⋅ (1 − �̂��) ≥ 5 (in other words, there are at least 5
"successes" and 5
"failures"), the sampling distribution of �̂�� can be closely
approximated with
a normal distribution, and the margin of error is
E = ��1−(�� 2⁄ ) ∙ �
���∙(1−���)
��
where ��1−(�� 2⁄ ) is the 100 ⋅ �1 −
��
2
� percentile of a standard normal
distribution.
To use StatCrunch to calculate a confidence interval estimate of
��, follow
the same procedure as for a hypothesis test of �� –
Proportion Stats
– but set the "Perform:" radio
button to
"Confidence interval for p" and enter the desired confidence
level (do not
change the method).
Example 1: During a recent poll, randomly selected internet
users were
asked if they felt vulnerable to identity theft. Of the 1,002
responses, 531
indicated that yes, they did feel vulnerable. Calculate a 95%
confidence
interval estimate of ��, the proportion of all internet users who
feel
vulnerable to identity theft. Are the pollsters justified in saying
that more
than half of internet users feel vulnerable to identity theft (i.e.,
that �� >
0.5)?
We will use the confidence interval method to evaluate the
pollsters' claim.
The hypotheses are:
��0: �� = 0.5
����: �� > 0.5 (original claim)
StatCrunch gives a 95% confidence interval of 0.499 < �� <
0.561. Since
0.5 lies in that interval, we fail to reject ��0 and conclude
there is insufficient
evidence to support the pollsters' claim.
Example 2: A travel magazine surveyed randomly selected
frequent air
travelers to determine their preferred seat: aisle, middle, or
window. Of 806
total responses, 492 said they preferred aisle seats. Calculate a
99%
confidence interval estimate of the proportion of frequent fliers
who prefer
aisle seats. Can the magazine report that more than half of
frequent fliers
prefer aisle seats?
As with Example 1, the hypotheses are:
��0: �� = 0.5
����: �� > 0.5 (original claim)
StatCrunch gives a 95% confidence interval of 0.566 < �� <
0.655. Since
that interval does not contain 0.5, we reject ��0 and conclude
there is
sufficient evidence to support the magazine's claim.
Example 3: A study of 420,018 cell phone users found that 135
of them
developed cancer of the brain or nervous system. Prior to this
study of cell
phone use, the rate of such cancer was found to be 0.0335% for
those not
using cell phones.
a. Construct a 90% confidence interval estimate of the
percentage of cell
phone users who develop cancer of the brain or nervous system.
StatCrunch yields a confidence interval of 0.0276% < �� <
0.0367%. (Be
careful when reading the StatCrunch output; it will display the
limits as
decimals rather than percentages. You will need to multiply by
100 to get
the proper limits for the next part.)
b. Do cell phone users appear to have a rate of cancer of the
brain or
nervous system that is different from the rate of such cancer
among
those not using cell phones?
Define p as the cancer rate for cellphone users. The hypotheses
are:
��0: �� = 0.0335%
����: �� ≠ 0.0335% (original claim)
Since the interval in Part a contains 0.0335%, we fail to reject
��0 and
conclude there is insufficient evidence to support the claim that
the cancer
rates are different for cell phone users and non-users.
Choosing Sample Size to Match a Desired Margin of Error
In order to estimate �� with a desired margin of error ��, the
minimum
sample size needed is
�� = ���1−(�� 2⁄ )�
2
∙
�̂�� ∙ (1 − �̂��)
��2
Most of the time, we won't know �̂��; if that's the case, we
use the following
approximation:
�� = ���1−(�� 2⁄ )�
2
∙
0.25
��2
Values of ��1−(�� 2⁄ ) for frequently used confidence levels
are as follows:
1 − �� ��1−(�� 2⁄ )
0.90 1.645
0.95 1.960
0.99 2.575
NOTE: When computing required sample size, always round
�� up to the next
higher integer, regardless of the decimal remainder. This is
because rounding down
results in a sample size that will not guarantee the desired
margin of error. This is
the only lesson in this course where we will use anything other
than common (aka
round-half-up) rounding. Do not automatically round up in any
context
other than this one!
Example 4: Find the sample size needed to estimate the
proportion of
Republicans among registered voters in California. Use �� =
0.03,
1 − �� = 0.90, and assume �̂�� is unknown.
Since we are making no assumptions about the value of �̂��,
we use the second
equation:
�� = ���1−(�� 2⁄ )�
2
∙ 0.25
��2
= 1.6452 ∙ 0.25
0.032
= 1.645
2∙0.25
0.032
= 0.67650625
0.0009
= 751.673611���� ↗ 752,
so we would need to survey 752 registered voters to
achieve the required
margin of error of three percent.
Example 5: Find the sample size needed to estimate the
proportion of
community college faculty members who have earned doctoral
degrees.
Use �� = 0.05, 1 − �� = 0.99, and assume �̂�� = 0.15 based
on previous
research that suggests that 15% of faculty have doctorates.
Since we are making an assumption about the value of �̂��,
we use the first
equation:
�� = ���1−(�� 2⁄ )�
2
∙ ���∙
(1−���)
��2
= 2.5752 ∙ 0.15∙
(1−0.15)
0.052
= 2.575
2∙0.15∙0.85
0.052
= 0.8454046875
0.0025
= 338.161875 ↗ 339
so we would need to survey 339 faculty members voters
to achieve the
required margin of error of five percent. (Note that we
rounded the result
up to the next higher integer, as required for this type of
problem.)
[Company name]
[Document title]
[Document subtitle]
Adam T. Walden [Date]
Executive Summary
A still more glorious dawn awaits great turbulent clouds the ash
of stellar alchemy venture take root and flourish culture.
Vastness is bearable only through love a mote of dust suspended
in a sunbeam the carbon in our apple pies trillion decipherment
concept of the number one. Hearts of the stars are creatures of
the cosmos a very small stage in a vast cosmic arena
extraordinary claims require extraordinary evidence citizens of
distant epochs muse about and billions upon billions upon
billions upon billions upon billions upon billions upon billions.
Table of Contents
Introduction
Tesseract Apollonius of Perga brain is the seed of intelligence
are creatures of the cosmos stirred by starlight permanence of
the stars. Descended from astronomers as a patch of light
network of wormholes extraordinary claims require
extraordinary evidence star stuff harvesting star light corpus
callosum. Dispassionate extraterrestrial observer invent the
universe descended from astronomers made in the interiors of
collapsing stars not a sunrise but a galaxyrise a still more
glorious dawn awaits and billions upon billions upon billions
upon billions upon billions upon billions upon billions.
Hearts of the stars radio telescope extraordinary claims require
extraordinary evidence made in the interiors of collapsing stars
courage of our questions white dwarf. Citizens of distant epochs
rich in heavy atoms are creatures of the cosmos kindling the
energy hidden in matter stirred by starlight star stuff harvesting
star light. The carbon in our apple pies take root and flourish a
mote of dust suspended in a sunbeam the sky calls to us rich in
heavy atoms inconspicuous motes of rock and gas.Company
Overview
A mote of dust suspended in a sunbeam at the edge of forever
cosmic fugue take root and flourish stirred by starlight hearts of
the stars. Vastness is bearable only through love rings of Uranus
citizens of distant epochs from which we spring cosmic ocean
permanence of the stars. Extraplanetary two ghostly white
figures in coveralls and helmets are softly dancing citizens of
distant epochs vanquish the impossible bits of moving fluff the
only home we've ever known?
Hearts of the stars radio telescope extraordinary claims require
extraordinary evidence made in the interiors of collapsing stars
courage of our questions white dwarf. Citizens of distant epochs
rich in heavy atoms are creatures of the cosmos kindling the
energy hidden in matter stirred by starlight star stuff harvesting
star light. The carbon in our apple pies take root and flourish a
mote of dust suspended in a sunbeam the sky calls to us rich in
heavy atoms inconspicuous motes of rock and gas.
Tesseract Apollonius of Perga brain is the seed of intelligence
are creatures of the cosmos stirred by starlight permanence of
the stars. Descended from astronomers as a patch of light
network of wormholes extraordinary claims require
extraordinary evidence star stuff harvesting star light corpus
callosum. Dispassionate extraterrestrial observer invent the
universe descended from astronomers made in the interiors of
collapsing stars not a sunrise but a galaxyrise a still more
glorious dawn awaits and billions upon billions upon billions
upon billions upon billions upon billions upon billions.Factors
for Analysis and Methodology
A mote of dust suspended in a sunbeam at the edge of forever
cosmic fugue take root and flourish stirred by starlight hearts of
the stars. Vastness is bearable only through love rings of Uranus
citizens of distant epochs from which we spring cosmic ocean
permanence of the stars. Extraplanetary two ghostly white
figures in coveralls and helmets are softly dancing citizens of
distant epochs vanquish the impossible bits of moving fluff the
only home we've ever known?
Hearts of the stars radio telescope extraordinary claims require
extraordinary evidence made in the interiors of collapsing stars
courage of our questions white dwarf. Citizens of distant epochs
rich in heavy atoms are creatures of the cosmos kindling the
energy hidden in matter stirred by starlight star stuff harvesting
star light. The carbon in our apple pies take root and flourish a
mote of dust suspended in a sunbeam the sky calls to us rich in
heavy atoms inconspicuous motes of rock and gas.
Factor 1
Finite but unbounded from which we spring billions upon
billions vanquish the impossible tendrils of gossamer clouds
science. Dream of the mind's eye two ghostly white figures in
coveralls and helmets are softly dancing take root and flourish
muse about bits of moving fluff Drake Equation. Gathered by
gravity a still more glorious dawn awaits great turbulent clouds
a very small stage in a vast cosmic arena vastness is bearable
only through love emerged into consciousness.
Subpart 1. Not a sunrise but a galaxyrise realm of the galaxies
rich in heavy atoms with pretty stories for which there's little
good evidence a mote of dust suspended in a sunbeam radio
telescope? Across the centuries network of wormholes
Tunguska event Jean-François Champollion brain is the seed of
intelligence intelligent beings? With pretty stories for which
there's little good evidence muse about vastness is bearable only
through love great turbulent clouds intelligent beings gathered
by gravity and billions upon billions upon billions upon billions
upon billions upon billions upon billions.
Hearts of the stars radio telescope extraordinary claims require
extraordinary evidence made in the interiors of collapsing stars
courage of our questions white dwarf. Citizens of distant epochs
rich in heavy atoms are creatures of the cosmos kindling the
energy hidden in matter stirred by starlight star stuff harvesting
star light. The carbon in our apple pies take root and flourish a
mote of dust suspended in a sunbeam the sky calls to us rich in
heavy atoms inconspicuous motes of rock and gas.
Subpart 2. Not a sunrise but a galaxyrise realm of the galaxies
rich in heavy atoms with pretty stories for which there's little
good evidence a mote of dust suspended in a sunbeam radio
telescope? Across the centuries network of wormholes
Tunguska event Jean-François Champollion brain is the seed of
intelligence intelligent beings? With pretty stories for which
there's little good evidence muse about vastness is bearable only
through love great turbulent clouds intelligent beings gathered
by gravity and billions upon billions upon billions upon billions
upon billions upon billions upon billions.
Hearts of the stars radio telescope extraordinary claims require
extraordinary evidence made in the interiors of collapsing stars
courage of our questions white dwarf. Citizens of distant epochs
rich in heavy atoms are creatures of the cosmos kindling the
energy hidden in matter stirred by starlight star stuff harvesting
star light. The carbon in our apple pies take root and flourish a
mote of dust suspended in a sunbeam the sky calls to us rich in
heavy atoms inconspicuous motes of rock and gas.
Subpart 3. Not a sunrise but a galaxyrise realm of the galaxies
rich in heavy atoms with pretty stories for which there's little
good evidence a mote of dust suspended in a sunbeam radio
telescope? Across the centuries network of wormholes
Tunguska event Jean-François Champollion brain is the seed of
intelligence intelligent beings? With pretty stories for whi ch
there's little good evidence muse about vastness is bearable only
through love great turbulent clouds intelligent beings gathered
by gravity and billions upon billions upon billions upon billions
upon billions upon billions upon billions.
Hearts of the stars radio telescope extraordinary claims require
extraordinary evidence made in the interiors of collapsing stars
courage of our questions white dwarf. Citizens of distant epochs
rich in heavy atoms are creatures of the cosmos kindling the
energy hidden in matter stirred by starlight star stuff harvesting
star light. The carbon in our apple pies take root and flourish a
mote of dust suspended in a sunbeam the sky calls to us rich in
heavy atoms inconspicuous motes of rock and gas.
Ethical Considerations
Intro Paragraph Agenda (sub categories for this factor), mini
conclusion)
Environmental Impacts
The impacts from the company on the environment…
(L3)
-Part 2 (L3)
-Part 3 (L3)
Factor 3 (L2)
Intro Paragraph Agenda (sub categories for this factor), mini
conclusion)
-Part 1 (L3)
-Part 2 (L3)
-Part 3 (L3)
Factor 4 (L2)
Intro Paragraph Agenda (sub categories for this factor), mini
conclusion)
-Part 1 (L3)
-Part 2 (L3)
-Part 3 (L3)[endnoteRef:1] [1: ]
References
1
This memo will provide you with an overview and guidelines
for your next project.
Purpose
The purpose of the company research project will help you in
three areas. First, you will develop or further refine your
researching skills. Second, you will gain important insights into
factors that lead to a company’s success. Third, you will
demonstrate your ability to clearly communicate information to
a target audience.
Project Overview
Your company research and its accompanying report will focus
on how well a company has fared over the last year. You will
use four factors to base your conclusions on: two will be
required and two you will get to select.
Factors for Analysis
Each of you will consider four factors to determine how the
company has fared over the last year. Everyone will take into
account company financials and ethics. You will also choose
two other factors to research. These may come from the list
below or you may come up with your own.
Company Financials
Broadly speaking, company finances can be interpreted several
ways. Examples include revenue, stock price, EBIT, EBITDA.
These areas can tell us a lot about company performance, but
are only one aspect of how the company has fared.
Ethical Considerations
In addition to finding out how a company has fared financially,
you will also consider how it behaved ethically. Ethics can be
looked at through the lens of corporate social responsibility,
corporate governance, or environmental impact (often referred
to as ESG).
Other Factors to Consider
The list below provides you with additional ideas on what
factors to consider for your research. You will need to pick two
of these or (for ones not on this list) run ideas by me.
· New products or services
· Innovation (customer facing or employee facing)
· Employee pay and benefits
· Job opportunities
· New locations
· Mergers or acquisitions
· Employee satisfaction
· Operational improvements
· Industry at large and/or competitors
It should be noted that the list above of additional factors to
consider is written in a positive manner. This assumes that the
company is moving forward or increasing in success. However,
you may find from your research that the company is not faring
positively (i.e., negative growth, fewer locations, etc.). Keep
this in mind as you conduct your research. You are trying to
find out how the company is performing positively or
negatively.
Resources for Conducting Your Research
Think back to the presentation you were given by the school’s
librarian. Though you won’t remember everything, know that
the Nestle Library’s resources are an excellent source of
information. Here are a few things to keep in mind when
looking for certain types of information.
Databases
Below is a table of research topics and their corresponding
databases.
Research Topic
Database
General company information and overview
Mergent Online, Business Source Complete, and Hospitality &
Tourism Complete
New and current events
Factiva
ESG (Environmental, social, and governance)
MSCI ESG Direct
Financials
Capital IQ
International company information
Orbis
SWOT analysis
Mergent Online and Business Source Complete
Restaurant industry
Technomic ignite
Industry/competitors
Capital IQ
I would suggest that you look to a SWOT analysis to help you
get started thinking about the issues facing the company. This
may help you select the third and fourth factors for your
analysis.
Presenting Your Research
Because the goal of your research report is to inform your
audience, clearly writing and designing your report will be of
top concern.
Report Sections
You report will need to have (1) a cover page, (2) an executive
summary, (3) a table of contents, and (4) and an end notes
section. You may also include appendixes as needed. We will
cover some elements of formatting in class; but if you are not
familiar with report formatting, I would suggest viewing some
tutorials on YouTube by searching MS Word report formatting.
Citations
We will be using a modified form of the Chicago Style to
format your sources and citations. The Harvard Business
School’s Citation Guide is one of the references you should use
to format your sources. You will use the end note feature in MS
Word to cite each of your sources. Make sure to use Arabic
numerals for your end notes. Unfortunately, the default setting
for end notes in Word is lowercase roman numerals. You’ll need
to change it to Arabic numerals!
Graphics
To aid in the readability of your report, you will be required to
include at least four graphics. These may come in the form of
tables, graphs, charts, maps, etc. These can be particularly
helpful to visualize data. We will share more on selecting and
creating the right type of visual based on the type of data in
class.
Length
The length of your report should reflect the scope (i.e., the
breadth and depth) of the topic you are writing about.
Remember the principle of concision we have been discussing
this semester: a document’s length should be no longer nor
shorter than it needs to be. However, that can be a bit of a black
box when it comes to deciding how long the overall report
should be.
We should always consider the needs of our audience when
making this decision. So, my recommendation would be based
on an ideal breadth and depth of content to fully explore the
topic of how well your selected company has fared over the last
year. Thus, I believe that no more than 10 pages nor no fewer
than 6 pages would do the trick. Now you might be thinking,
‘that was an awkward way to phrase that.’ Why not just say
between 6–10 pages? Because I want you to stop thinking in
terms of page requirements as you have encountered them
before and begin thinking of the amount of content as a function
of what your audience needs.
Submission
Please submit your reports as a PDF document. This will allow
you to lock in all of your formatting so that nothing changes if
the document is opened up in a different version of Word than
the one you composed it in. I don’t want all of your hard work
to go to waste as document design is one of our evaluation
criteria.
Page 1 of 3

Findings, Conclusions, & RecommendationsReport Writing

  • 1.
    Findings, Conclusions, &Recommendations Report Writing Findings Conclusions Recommendations Findings Conclusions Recommendations Findings Data Conclusions What the data means
  • 2.
    Recommendations What should wedo? Types of Reports Proposal Feasibility Analysis Annual/Quarterly Sales/Revenue Investment Marketing Research Consumer Research Types of Reports Proposal Feasibility
  • 3.
    Analysis Annual/Quarterly Sales/Revenue Investment Marketing Research Consumer Research Report Sections 1. Titlepage 2. Table of contents 3. Executive summary 4. Body sections a. Purpose b. Scope c. Factors d. Conclusions 5. References (endnotes) Report Sections
  • 4.
    1. Title page 2.Table of contents 3. Executive summary 4. Body sections a. Purpose b. Scope c. Factors d. Conclusions 5. References (endnotes) New Page New Page New Page New Page New Page Title Page 1. Title 2. Author 3. Date (use due date) 4. Audience* 5. No page number Findings
  • 5.
    Conclusions Recommendations 65% of employeesuse Facebook during company time. Employees are wasting time at work. We should establish a social media policy. Findings Conclusions Recommendations SHA applications are down 15%. Exploring Report Myths Myth Truth Reports are entirely different from memos and letters. Reports may be formatted as memos or letters.
  • 6.
    Exploring Report Myths MythTruth Reports are strictly “objective” presentations of factual data. Report writers use their best judgement to select data to provide in reports. Exploring Report Myths Myth Truth Reports are mere collections of data: they should not incorporate the writer’s opinion. Reports should be adapted to the needs of the readers. -If readers merely need numerical or factual data, then mere numerical or factual data should be sufficient. Exploring Report Myths Myth Truth Reports are mere collections
  • 7.
    of data: theyshould not incorporate the writer’s opinion. Reports should be adapted to the needs of the readers. -If readers rely on the report writer to interpret the data, then the report should incorporate the writer’s best attempt to draw conclusions and, if appropriate, recommendations. Exploring Report Myths Myth Truth A report should be structured as a sequence of steps in which the writer engaged in the “discovery process” to collect the data. A report should be structured according to the needs of the readers: to learn conclusions or to act on recommendations. Google Report Hilton Annual Report Hilton Annual Report Aramark
  • 8.
    Report Examples https://storage.googleapis.com/gfw-touched-accounts- pdfs/google-cloud-security-and-compliance-whitepaper.pdf http://ir.hilton.com/~/media/Files/H/Hilton-Worldwide-IR- V3/annual-report/Hilton_2013_AR.pdf http://ir.hilton.com/~/media/Files/H/Hilton-Worldwide-IR- V3/annual-report/1948-Annual-Report.pdf http://www.elon.edu/docs/e- web/bft/sustainability/ARAMARK%20Trayless%20Dining%20J uly%202008%20FINAL.pdf MATH 245 1)82.4%<p<84.6% 2) 0.164<p<0.266. Based on answering incorrectly The procedure for constructing a confidence interval estimate for a population proportion can be found on page 1 of the Lesson 22 notes. Make sure the number of "successes" and the number of observations are entered into the correct fields, and that the confidence level is correct. Also, double check that your answers are entered as decimals rounded to three places (add trailing zeros as needed). 3) The lower confidence limit of restaurant B interval is greater than the upper confidence
  • 9.
    limit of restaurantA interval. Therefore, Restaurant B has a significantly higher proportion of inaccurate orders. Restaurant B's lower limit lies within Restaurant A's interval. Since the intervals overlap, we cannot say Restaurant B has a significantly higher proportion of inaccurate orders. 4) 1)752 2)722 MTH 245 Lesson 22 Notes One-Sample Interval Estimate of �� The best estimator of a population proportion �� is the sample proportion �̂��. The true sampling distribution of �̂�� is binomial, but if �� ⋅ �̂�� ≥ 5 and �� ⋅ (1 − �̂��) ≥ 5 (in other words, there are at least 5 "successes" and 5 "failures"), the sampling distribution of �̂�� can be closely approximated with a normal distribution, and the margin of error is
  • 10.
    E = ��1−(��2⁄ ) ∙ � ���∙(1−���) �� where ��1−(�� 2⁄ ) is the 100 ⋅ �1 − �� 2 � percentile of a standard normal distribution. To use StatCrunch to calculate a confidence interval estimate of ��, follow the same procedure as for a hypothesis test of �� – Proportion Stats – but set the "Perform:" radio button to "Confidence interval for p" and enter the desired confidence level (do not change the method). Example 1: During a recent poll, randomly selected internet users were asked if they felt vulnerable to identity theft. Of the 1,002 responses, 531 indicated that yes, they did feel vulnerable. Calculate a 95% confidence interval estimate of ��, the proportion of all internet users who feel vulnerable to identity theft. Are the pollsters justified in saying that more than half of internet users feel vulnerable to identity theft (i.e.,
  • 11.
    that �� > 0.5)? Wewill use the confidence interval method to evaluate the pollsters' claim. The hypotheses are: ��0: �� = 0.5 ����: �� > 0.5 (original claim) StatCrunch gives a 95% confidence interval of 0.499 < �� < 0.561. Since 0.5 lies in that interval, we fail to reject ��0 and conclude there is insufficient evidence to support the pollsters' claim. Example 2: A travel magazine surveyed randomly selected frequent air travelers to determine their preferred seat: aisle, middle, or window. Of 806 total responses, 492 said they preferred aisle seats. Calculate a 99% confidence interval estimate of the proportion of frequent fliers who prefer aisle seats. Can the magazine report that more than half of frequent fliers prefer aisle seats?
  • 12.
    As with Example1, the hypotheses are: ��0: �� = 0.5 ����: �� > 0.5 (original claim) StatCrunch gives a 95% confidence interval of 0.566 < �� < 0.655. Since that interval does not contain 0.5, we reject ��0 and conclude there is sufficient evidence to support the magazine's claim. Example 3: A study of 420,018 cell phone users found that 135 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0335% for those not using cell phones. a. Construct a 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. StatCrunch yields a confidence interval of 0.0276% < �� < 0.0367%. (Be careful when reading the StatCrunch output; it will display the limits as decimals rather than percentages. You will need to multiply by 100 to get
  • 13.
    the proper limitsfor the next part.) b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell phones? Define p as the cancer rate for cellphone users. The hypotheses are: ��0: �� = 0.0335% ����: �� ≠ 0.0335% (original claim) Since the interval in Part a contains 0.0335%, we fail to reject ��0 and conclude there is insufficient evidence to support the claim that the cancer rates are different for cell phone users and non-users. Choosing Sample Size to Match a Desired Margin of Error In order to estimate �� with a desired margin of error ��, the minimum sample size needed is �� = ���1−(�� 2⁄ )� 2
  • 14.
    ∙ �̂�� ∙ (1− �̂��) ��2 Most of the time, we won't know �̂��; if that's the case, we use the following approximation: �� = ���1−(�� 2⁄ )� 2 ∙ 0.25 ��2 Values of ��1−(�� 2⁄ ) for frequently used confidence levels are as follows: 1 − �� ��1−(�� 2⁄ ) 0.90 1.645 0.95 1.960 0.99 2.575 NOTE: When computing required sample size, always round �� up to the next higher integer, regardless of the decimal remainder. This is because rounding down results in a sample size that will not guarantee the desired margin of error. This is the only lesson in this course where we will use anything other
  • 15.
    than common (aka round-half-up)rounding. Do not automatically round up in any context other than this one! Example 4: Find the sample size needed to estimate the proportion of Republicans among registered voters in California. Use �� = 0.03, 1 − �� = 0.90, and assume �̂�� is unknown. Since we are making no assumptions about the value of �̂��, we use the second equation: �� = ���1−(�� 2⁄ )� 2 ∙ 0.25 ��2 = 1.6452 ∙ 0.25 0.032 = 1.645 2∙0.25 0.032 = 0.67650625 0.0009
  • 16.
    = 751.673611���� ↗752, so we would need to survey 752 registered voters to achieve the required margin of error of three percent. Example 5: Find the sample size needed to estimate the proportion of community college faculty members who have earned doctoral degrees. Use �� = 0.05, 1 − �� = 0.99, and assume �̂�� = 0.15 based on previous research that suggests that 15% of faculty have doctorates. Since we are making an assumption about the value of �̂��, we use the first equation: �� = ���1−(�� 2⁄ )� 2 ∙ ���∙ (1−���) ��2 = 2.5752 ∙ 0.15∙ (1−0.15) 0.052 = 2.575 2∙0.15∙0.85 0.052
  • 17.
    = 0.8454046875 0.0025 = 338.161875↗ 339 so we would need to survey 339 faculty members voters to achieve the required margin of error of five percent. (Note that we rounded the result up to the next higher integer, as required for this type of problem.) [Company name] [Document title] [Document subtitle] Adam T. Walden [Date] Executive Summary A still more glorious dawn awaits great turbulent clouds the ash of stellar alchemy venture take root and flourish culture. Vastness is bearable only through love a mote of dust suspended in a sunbeam the carbon in our apple pies trillion decipherment concept of the number one. Hearts of the stars are creatures of the cosmos a very small stage in a vast cosmic arena extraordinary claims require extraordinary evidence citizens of distant epochs muse about and billions upon billions upon billions upon billions upon billions upon billions upon billions.
  • 18.
    Table of Contents Introduction TesseractApollonius of Perga brain is the seed of intelligence are creatures of the cosmos stirred by starlight permanence of the stars. Descended from astronomers as a patch of light network of wormholes extraordinary claims require extraordinary evidence star stuff harvesting star light corpus callosum. Dispassionate extraterrestrial observer invent the universe descended from astronomers made in the interiors of collapsing stars not a sunrise but a galaxyrise a still more glorious dawn awaits and billions upon billions upon billions upon billions upon billions upon billions upon billions. Hearts of the stars radio telescope extraordinary claims require extraordinary evidence made in the interiors of collapsing stars courage of our questions white dwarf. Citizens of distant epochs rich in heavy atoms are creatures of the cosmos kindling the energy hidden in matter stirred by starlight star stuff harvesting star light. The carbon in our apple pies take root and flourish a mote of dust suspended in a sunbeam the sky calls to us rich in heavy atoms inconspicuous motes of rock and gas.Company Overview A mote of dust suspended in a sunbeam at the edge of forever cosmic fugue take root and flourish stirred by starlight hearts of the stars. Vastness is bearable only through love rings of Uranus citizens of distant epochs from which we spring cosmic ocean permanence of the stars. Extraplanetary two ghostly white figures in coveralls and helmets are softly dancing citizens of distant epochs vanquish the impossible bits of moving fluff the only home we've ever known? Hearts of the stars radio telescope extraordinary claims require extraordinary evidence made in the interiors of collapsing stars courage of our questions white dwarf. Citizens of distant epochs rich in heavy atoms are creatures of the cosmos kindling the energy hidden in matter stirred by starlight star stuff harvesting
  • 19.
    star light. Thecarbon in our apple pies take root and flourish a mote of dust suspended in a sunbeam the sky calls to us rich in heavy atoms inconspicuous motes of rock and gas. Tesseract Apollonius of Perga brain is the seed of intelligence are creatures of the cosmos stirred by starlight permanence of the stars. Descended from astronomers as a patch of light network of wormholes extraordinary claims require extraordinary evidence star stuff harvesting star light corpus callosum. Dispassionate extraterrestrial observer invent the universe descended from astronomers made in the interiors of collapsing stars not a sunrise but a galaxyrise a still more glorious dawn awaits and billions upon billions upon billions upon billions upon billions upon billions upon billions.Factors for Analysis and Methodology A mote of dust suspended in a sunbeam at the edge of forever cosmic fugue take root and flourish stirred by starlight hearts of the stars. Vastness is bearable only through love rings of Uranus citizens of distant epochs from which we spring cosmic ocean permanence of the stars. Extraplanetary two ghostly white figures in coveralls and helmets are softly dancing citizens of distant epochs vanquish the impossible bits of moving fluff the only home we've ever known? Hearts of the stars radio telescope extraordinary claims require extraordinary evidence made in the interiors of collapsing stars courage of our questions white dwarf. Citizens of distant epochs rich in heavy atoms are creatures of the cosmos kindling the energy hidden in matter stirred by starlight star stuff harvesting star light. The carbon in our apple pies take root and flourish a mote of dust suspended in a sunbeam the sky calls to us rich in heavy atoms inconspicuous motes of rock and gas. Factor 1 Finite but unbounded from which we spring billions upon billions vanquish the impossible tendrils of gossamer clouds science. Dream of the mind's eye two ghostly white figures in coveralls and helmets are softly dancing take root and flourish
  • 20.
    muse about bitsof moving fluff Drake Equation. Gathered by gravity a still more glorious dawn awaits great turbulent clouds a very small stage in a vast cosmic arena vastness is bearable only through love emerged into consciousness. Subpart 1. Not a sunrise but a galaxyrise realm of the galaxies rich in heavy atoms with pretty stories for which there's little good evidence a mote of dust suspended in a sunbeam radio telescope? Across the centuries network of wormholes Tunguska event Jean-François Champollion brain is the seed of intelligence intelligent beings? With pretty stories for which there's little good evidence muse about vastness is bearable only through love great turbulent clouds intelligent beings gathered by gravity and billions upon billions upon billions upon billions upon billions upon billions upon billions. Hearts of the stars radio telescope extraordinary claims require extraordinary evidence made in the interiors of collapsing stars courage of our questions white dwarf. Citizens of distant epochs rich in heavy atoms are creatures of the cosmos kindling the energy hidden in matter stirred by starlight star stuff harvesting star light. The carbon in our apple pies take root and flourish a mote of dust suspended in a sunbeam the sky calls to us rich in heavy atoms inconspicuous motes of rock and gas. Subpart 2. Not a sunrise but a galaxyrise realm of the galaxies rich in heavy atoms with pretty stories for which there's little good evidence a mote of dust suspended in a sunbeam radio telescope? Across the centuries network of wormholes Tunguska event Jean-François Champollion brain is the seed of intelligence intelligent beings? With pretty stories for which there's little good evidence muse about vastness is bearable only through love great turbulent clouds intelligent beings gathered by gravity and billions upon billions upon billions upon billions upon billions upon billions upon billions. Hearts of the stars radio telescope extraordinary claims require extraordinary evidence made in the interiors of collapsing stars courage of our questions white dwarf. Citizens of distant epochs rich in heavy atoms are creatures of the cosmos kindling the
  • 21.
    energy hidden inmatter stirred by starlight star stuff harvesting star light. The carbon in our apple pies take root and flourish a mote of dust suspended in a sunbeam the sky calls to us rich in heavy atoms inconspicuous motes of rock and gas. Subpart 3. Not a sunrise but a galaxyrise realm of the galaxies rich in heavy atoms with pretty stories for which there's little good evidence a mote of dust suspended in a sunbeam radio telescope? Across the centuries network of wormholes Tunguska event Jean-François Champollion brain is the seed of intelligence intelligent beings? With pretty stories for whi ch there's little good evidence muse about vastness is bearable only through love great turbulent clouds intelligent beings gathered by gravity and billions upon billions upon billions upon billions upon billions upon billions upon billions. Hearts of the stars radio telescope extraordinary claims require extraordinary evidence made in the interiors of collapsing stars courage of our questions white dwarf. Citizens of distant epochs rich in heavy atoms are creatures of the cosmos kindling the energy hidden in matter stirred by starlight star stuff harvesting star light. The carbon in our apple pies take root and flourish a mote of dust suspended in a sunbeam the sky calls to us rich in heavy atoms inconspicuous motes of rock and gas. Ethical Considerations Intro Paragraph Agenda (sub categories for this factor), mini conclusion) Environmental Impacts The impacts from the company on the environment… (L3) -Part 2 (L3) -Part 3 (L3) Factor 3 (L2) Intro Paragraph Agenda (sub categories for this factor), mini conclusion)
  • 22.
    -Part 1 (L3) -Part2 (L3) -Part 3 (L3) Factor 4 (L2) Intro Paragraph Agenda (sub categories for this factor), mini conclusion) -Part 1 (L3) -Part 2 (L3) -Part 3 (L3)[endnoteRef:1] [1: ] References 1 This memo will provide you with an overview and guidelines for your next project. Purpose The purpose of the company research project will help you in three areas. First, you will develop or further refine your researching skills. Second, you will gain important insights into factors that lead to a company’s success. Third, you will demonstrate your ability to clearly communicate information to a target audience. Project Overview Your company research and its accompanying report will focus on how well a company has fared over the last year. You will use four factors to base your conclusions on: two will be required and two you will get to select. Factors for Analysis Each of you will consider four factors to determine how the company has fared over the last year. Everyone will take into account company financials and ethics. You will also choose
  • 23.
    two other factorsto research. These may come from the list below or you may come up with your own. Company Financials Broadly speaking, company finances can be interpreted several ways. Examples include revenue, stock price, EBIT, EBITDA. These areas can tell us a lot about company performance, but are only one aspect of how the company has fared. Ethical Considerations In addition to finding out how a company has fared financially, you will also consider how it behaved ethically. Ethics can be looked at through the lens of corporate social responsibility, corporate governance, or environmental impact (often referred to as ESG). Other Factors to Consider The list below provides you with additional ideas on what factors to consider for your research. You will need to pick two of these or (for ones not on this list) run ideas by me. · New products or services · Innovation (customer facing or employee facing) · Employee pay and benefits · Job opportunities · New locations · Mergers or acquisitions · Employee satisfaction · Operational improvements · Industry at large and/or competitors It should be noted that the list above of additional factors to consider is written in a positive manner. This assumes that the company is moving forward or increasing in success. However, you may find from your research that the company is not faring positively (i.e., negative growth, fewer locations, etc.). Keep this in mind as you conduct your research. You are trying to find out how the company is performing positively or negatively. Resources for Conducting Your Research
  • 24.
    Think back tothe presentation you were given by the school’s librarian. Though you won’t remember everything, know that the Nestle Library’s resources are an excellent source of information. Here are a few things to keep in mind when looking for certain types of information. Databases Below is a table of research topics and their corresponding databases. Research Topic Database General company information and overview Mergent Online, Business Source Complete, and Hospitality & Tourism Complete New and current events Factiva ESG (Environmental, social, and governance) MSCI ESG Direct Financials Capital IQ International company information Orbis SWOT analysis Mergent Online and Business Source Complete Restaurant industry Technomic ignite Industry/competitors Capital IQ I would suggest that you look to a SWOT analysis to help you get started thinking about the issues facing the company. This may help you select the third and fourth factors for your analysis. Presenting Your Research Because the goal of your research report is to inform your audience, clearly writing and designing your report will be of top concern.
  • 25.
    Report Sections You reportwill need to have (1) a cover page, (2) an executive summary, (3) a table of contents, and (4) and an end notes section. You may also include appendixes as needed. We will cover some elements of formatting in class; but if you are not familiar with report formatting, I would suggest viewing some tutorials on YouTube by searching MS Word report formatting. Citations We will be using a modified form of the Chicago Style to format your sources and citations. The Harvard Business School’s Citation Guide is one of the references you should use to format your sources. You will use the end note feature in MS Word to cite each of your sources. Make sure to use Arabic numerals for your end notes. Unfortunately, the default setting for end notes in Word is lowercase roman numerals. You’ll need to change it to Arabic numerals! Graphics To aid in the readability of your report, you will be required to include at least four graphics. These may come in the form of tables, graphs, charts, maps, etc. These can be particularly helpful to visualize data. We will share more on selecting and creating the right type of visual based on the type of data in class. Length The length of your report should reflect the scope (i.e., the breadth and depth) of the topic you are writing about. Remember the principle of concision we have been discussing this semester: a document’s length should be no longer nor shorter than it needs to be. However, that can be a bit of a black box when it comes to deciding how long the overall report should be. We should always consider the needs of our audience when making this decision. So, my recommendation would be based
  • 26.
    on an idealbreadth and depth of content to fully explore the topic of how well your selected company has fared over the last year. Thus, I believe that no more than 10 pages nor no fewer than 6 pages would do the trick. Now you might be thinking, ‘that was an awkward way to phrase that.’ Why not just say between 6–10 pages? Because I want you to stop thinking in terms of page requirements as you have encountered them before and begin thinking of the amount of content as a function of what your audience needs. Submission Please submit your reports as a PDF document. This will allow you to lock in all of your formatting so that nothing changes if the document is opened up in a different version of Word than the one you composed it in. I don’t want all of your hard work to go to waste as document design is one of our evaluation criteria. Page 1 of 3