Lecture5 Applied Econometrics and Economic Modeling
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The document discusses various statistical techniques for constructing confidence intervals from sample data. It provides examples of calculating 95% confidence intervals for a mean, proportion, difference between means, and difference between proportions. It also discusses how to determine the necessary sample size needed to achieve a given confidence interval length.
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Annual/Quarterly
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Investment
Marketing
Research
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1. Title page
2. Table of contents
3. Executive summary
4. Body sections
a. Purpose
b. Scope
c. Factors
d. Conclusions
5. References (endnotes)
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1. Title page
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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.
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Section 7 Analyzing our Marketing Test, Survey Results .docx
Section 7
Analyzing our Marketing Test, Survey Results
and Other Metrics Using Confidence Intervals
Rhonda Knehans Drake
Associate Professor, New York University
Data Analytics, Interpretation and Reporting
copyright © 2013
2
• When we estimate population averages or percentages based on
samples, a certain amount of error is present.
• The amount of error present is a function mostly of your
sample size.
• The larger the sample, the less error in your estimates.
• Today we will learn how to place bounds around our estimates
obtained.
• With such an interval, we will then be able to say with 90%, 95%
or 99% confidence that the true population estimate will lie in
these bounds.
Introduction
3
The eight confidence interval formulas we will discuss are for
the following situations:
1. Average or mean based on large samples
2. Average or mean based on small samples
3. Response rate or survey percent based on large samples
4. Response rate or survey percent based on small samples
5. Difference between 2 averages for large samples
6. Difference between 2 averages for small samples
7. Difference between 2 response rates for large samples
8. Difference between 2 response rates for small sample
Confidence Intervals
A-B Split Tests
4
1. Confidence Interval for Averages or Means Based on
Large Samples (n ≥ 30)
To calculate a confidence interval around a mean, the following
information is required:
– The sample mean x obtained from the test.
– The sample standard deviation S obtained from the test.
Many software packages, including Microsoft ExcelTM, can
automatically calculate this value for you. (Review Section 3 for the
standard deviation formula.)
– The sample size n of the test.
This is the number of observations used to calculate your mean. The
sample size must be greater than or equal to 30 in size.
– The desired confidence level: 90%, 95% or 99%.
A confidence interval constructed around the mean will guarantee, with
your specified level of confidence, the true mean will fall within those
bounds.
Sample Means
(Large Sample)
5
• Once all information is known, you construct the confidence
interval around the mean by adding and subtracting from the
mean a multiple of your standard deviation associated with the
sample mean. The “multiple” depends on your desired
confidence level.
• The formula for a confidence interval around the mean is
calculated as follows:
x (Z )(S/n )
Where:
• S is the standard deviation associated with the sample.
• n is the sample size.
• Z is equal to 1.645, 1.96 or 2.575 for a 90%, 95% or 99%
confidence level
Sample Means
(Large Sample)
6
Example:
Money magazine conducts a survey of 100 retirees across the US
and asks them how much they have in their retirement fund.
You obtain an average of $84.75 with a standard deviation of
$18.75, both in thousands of doll.
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The idea of reviewing the data is to come up with a implementable framework and establish protocols which will enable visibility of machine health status and proactively take remedial steps before an actual breakdown. Post analysis the summary and recommendations are given below:
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In the interim, mandate monthly review of all Provider 3 machines aged more than 60 months.
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Findings, Conclusions, & RecommendationsReport Writing
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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
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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)
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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
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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.
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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
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Section 7 Analyzing our Marketing Test, Survey Results .docx
Section 7
Analyzing our Marketing Test, Survey Results
and Other Metrics Using Confidence Intervals
Rhonda Knehans Drake
Associate Professor, New York University
Data Analytics, Interpretation and Reporting
copyright © 2013
2
• When we estimate population averages or percentages based on
samples, a certain amount of error is present.
• The amount of error present is a function mostly of your
sample size.
• The larger the sample, the less error in your estimates.
• Today we will learn how to place bounds around our estimates
obtained.
• With such an interval, we will then be able to say with 90%, 95%
or 99% confidence that the true population estimate will lie in
these bounds.
Introduction
3
The eight confidence interval formulas we will discuss are for
the following situations:
1. Average or mean based on large samples
2. Average or mean based on small samples
3. Response rate or survey percent based on large samples
4. Response rate or survey percent based on small samples
5. Difference between 2 averages for large samples
6. Difference between 2 averages for small samples
7. Difference between 2 response rates for large samples
8. Difference between 2 response rates for small sample
Confidence Intervals
A-B Split Tests
4
1. Confidence Interval for Averages or Means Based on
Large Samples (n ≥ 30)
To calculate a confidence interval around a mean, the following
information is required:
– The sample mean x obtained from the test.
– The sample standard deviation S obtained from the test.
Many software packages, including Microsoft ExcelTM, can
automatically calculate this value for you. (Review Section 3 for the
standard deviation formula.)
– The sample size n of the test.
This is the number of observations used to calculate your mean. The
sample size must be greater than or equal to 30 in size.
– The desired confidence level: 90%, 95% or 99%.
A confidence interval constructed around the mean will guarantee, with
your specified level of confidence, the true mean will fall within those
bounds.
Sample Means
(Large Sample)
5
• Once all information is known, you construct the confidence
interval around the mean by adding and subtracting from the
mean a multiple of your standard deviation associated with the
sample mean. The “multiple” depends on your desired
confidence level.
• The formula for a confidence interval around the mean is
calculated as follows:
x (Z )(S/n )
Where:
• S is the standard deviation associated with the sample.
• n is the sample size.
• Z is equal to 1.645, 1.96 or 2.575 for a 90%, 95% or 99%
confidence level
Sample Means
(Large Sample)
6
Example:
Money magazine conducts a survey of 100 retirees across the US
and asks them how much they have in their retirement fund.
You obtain an average of $84.75 with a standard deviation of
$18.75, both in thousands of doll.
Descriptive Statistics and Interpretation Grading GuideQNT5.docx
Descriptive Statistics and Interpretation Grading Guide
QNT/561 Version 7
1
Individual Assignment: Descriptive Statistics and Interpretation
Purpose of Assignment
The purpose of this assignment is to guide students on how to describe large amounts of data in a way that is understandable, useful, and, if need be, convincing, using descriptive statistics summaries of central tendency and variability.
Resources Required
· Ch. 15, 16, & 19 of Business Research Methods
· Individual Methodology Findings Template
· Descriptive Statistics and Interpretation Example
Grading Guide
Content
70 Percent
Met
Partially
Met
Not Met
Comments:
Creation of a Microsoft® Excel® spreadsheet with the two variables from your learning team’s dataset.
Analysis of the data with MegaStat®, StatCrunch®, Microsoft® Excel® or other statistical tool(s), and includes the following:
(a) Descriptive stats for each numeric variable
(b) Histogram for each numeric variable
(c) Bar chart for each attribute (non numeric) variable
(d) Scatter plot if the data contains two numeric variables
Use of the Individual Methodology Findings Template to complete the descriptive statistics.
Determination of the appropriate descriptive statistics which included one of the following:
(a) For normally distributed data use the mean and standard deviation.
(b) For significantly skewed data use the median and interquartile range.
Use of the Descriptive Statistics and Interpretation Example to develop an interpretation of the descriptive statistics.
Both the spreadsheet and the completed Individual Methodology Findings Template were submitted.
Total
Available
Total
Earned
3.5
#/3.5
Writing Guidelines
30 Percent
Met
Partially
Met
Not Met
Comments:
The paper—including tables and graphs, headings, title page, and reference page—is consistent with APA formatting guidelines and meets course-level requirements.
Intellectual property is recognized with in-text citations and a reference page.
Paragraph and sentence transitions are present, logical, and maintain the flow throughout the synopsis.
Sentences are complete, clear, and concise.
Rules of grammar and usage are followed including spelling and punctuation.
Total
Available
Total
Earned
1.5
#/1.5
Assignment Total
#
5
#/5
Additional comments:
Copyright © 2013, 2012, 2011, 2009, 2008 by University of Phoenix. All rights reserved.
Sampling and Data Collection Plan
SAMPLING AND DATA COLLECTION PLAN
1
SAMPLING AND DATA COLLECTION PLAN
11
QNT 561 Business Research & Statistics
Sampling and Data Collection Plan
Introduction
This paper outlines the sampling and data collection procedure. The sampling will be used to test the null hypothesis against the alternate hypothesis:
H0: Implementing Total Quality Management (TQM) will not increase product quality.
HA: Implementing Total Quality Management (TQM) will increase product quality.
A good qualitati.
Jigsaw Academy Pexitics Student Projects
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Jigsaw Corporate Contest: Pexitics Preventive Maintenance Case Study
The winning presentation of the Jigsaw Academy Corporate Contest.
Brief Description of the case study:
A company which produces corrugated boxes with honeycomb pattern wants to build a model to predict breakdown and use preventive maintenance to reduce downtime (time during which production is stopped especially during setup for an operation or when making repairs). The dataset provided had 90000 instances of maintenance work done across 1 year across various machines. Jigsaw Students were expected to analyze the data and check if the data was consistent across various teams and providers, does one need to analyze across various segments (teams/providers/any other), if so how should the segmentation be done and how can various rules be created across pressure levels and lifetime of a machine to predict the breakage.
Module 7 Interval estimatorsMaster for Business Statistics.docx
Module 7
Interval estimators
Master for Business Statistics
Dane McGuckian
Topics
7.1 Interval Estimate of the Population Mean with a Known Population Standard Deviation
7.2 Sample Size Requirements for Estimating the Population Mean
7.3 Interval Estimate of the Population Mean with an Unknown Population Standard Deviation
7.4 Interval Estimate of the Population Proportion
7.5 Sample Size Requirements for Estimating the Population Proportion
7.1
Interval Estimate of the Population Mean with a Known Population Standard Deviation
Interval Estimators
Quantities like the sample mean and the sample standard deviation are called point estimators because they are single values derived from sample data that are used to estimate the value of an unknown population parameter.
The point estimators used in Statistics have some very desirable traits; however, they do not come with a measure of certainty.
In other words, there is no way to determine how close the population parameter is to a value of our point estimate. For this reason, the interval estimator was developed.
An interval estimator is a range of values derived from sample data that has a certain probability of containing the population parameter.
This probability is usually referred to as confidence, and it is the main advantage that interval estimators have over point estimators.
The confidence level for a confidence interval tells us the likelihood that a given interval will contain the target parameter we are trying to estimate.
The Meaning of “Confidence Level”
Interval estimates come with a level of confidence.
The level of confidence is specified by its confidence coefficient – it is the probability (relative frequency) that an interval estimator will enclose the target parameter when the estimator is used repeatedly a very large number of times.
The most common confidence levels are 99%, 98%, 95%, and 90%.
Example: A manufacturer takes a random sample of 40 computer chips from its production line to construct a 95% confidence interval to estimate the true average lifetime of the chip. If the manufacturer formed confidence intervals for every possible sample of 40 chips, 95% of those intervals would contain the population average.
The Meaning of “Confidence Level”
In the previous example, it is important to note that once the manufacturer has constructed a 95% confidence interval, it is no longer acceptable to state that there is a 95% chance that the interval contains the true average lifetime of the computer chip.
Prior to constructing the interval, there was a 95% chance that the random interval limits would contain the true average, but once the process of collecting the sample and constructing the interval is complete, the resulting interval either does or does not contain the true average.
Thus there is a probability of 1 or 0 that the true average is contained within the interval, not a 0.95 probability.
The interval limits are random variables because the ...
As mentioned earlier, the mid-term will have conceptual and quanti.docx
As mentioned earlier, the mid-term will have conceptual and quantitative multiple-choice questions. You need to read all 4 chapters and you need to be able to solve problems in all 4 chapters in order to do well in this test.
The following are for review and learning purposes only. I am not indicating that identical or similar problems will be in the test. As I have indicated in the class syllabus, all the exams in this course will have multiple-choice questions and problems.
Suggestion: treat this review set as you would an actual test. Sit down with your one page of notes and your calculator, and give it a try. That way you will know what areas you still need to study.
ADMN 210
Answers to Review for Midterm #1
1) Classify each of the following as nominal, ordinal, interval, or ratio data.
a. The time required to produce each tire on an assembly line – ratio since it is numeric with a valid 0 point meaning “lack of”
b. The number of quarts of milk a family drinks in a month - ratio since it is numeric with a valid 0 point meaning “lack of”
c. The ranking of four machines in your plant after they have been designated as excellent, good, satisfactory, and poor – ordinal since it is ranking data only
d. The telephone area code of clients in the United States – nominal since it is a label
e. The age of each of your employees - ratio since it is numeric with a valid 0 point meaning “lack of”
f. The dollar sales at the local pizza house each month - ratio since it is numeric with a valid 0 point meaning “lack of”
g. An employee’s identification number – nominal since it is a label
h. The response time of an emergency unit - ratio since it is numeric with a valid 0 point meaning “lack of”
2) True or False: The highest level of data measurement is the ratio-level measurement.
True (you can do the most powerful analysis with this kind of data)
3) True or False: Interval- and ratio-level data are also referred to as categorical data.
False (Interval and ratio level data are numeric and therefore quantitative, NOT qualitative….Nominal is qualitative)
4) A small portion or a subset of the population on which data is collected for conducting statistical analysis is called __________.
A sample! A population is the total group, a census IS the population, and a data set can be either a sample or a population.
5) One of the advantages for taking a sample instead of conducting a census is this:
a sample is more accurate than census
a sample is difficult to take
a sample cannot be trusted
a sample can save money when data collection process is destructive
6) Selection of the winning numbers is a lottery is an example of __________.
convenience sampling
random sampling
nonrandom sampling
regulatory sampling
7) A type of random sampling in which the population is divided into non-overlapping subpopulations is called __________.
stratified random sampling
cluster sampling
systematic random sampling
regulatory sampling
8) A ...
Statistics Homework Help
I am Hannah Dennis. Currently associated with excelhomeworkhelp.com as Excel homework helper. After completing my master's from Kean University, USA. I was in search of an opportunity that expands my area of knowledge hence I decided to help students with their homework. I have written several excel homework till date to help students overcome numerous difficulties they face.
5 simple questions to determin sample size
The goal of this write-up is to provide you a simple overview of how to determine sample size for your survey or A/B testing.
Quantitative MethodsChoosing a Sample.pptxChoosing a Samp.docx
Quantitative Methods/Choosing a Sample.pptx
Choosing a Sample
Leedy, P., and Ormrod, J., Practical Research. (8th ed.)
Fink, A. 1995. From the Survey Toolkit published by Sage.
Choosing a Sample to Survey
Population – the group to be covered by your research plan
Sample – a subset of your population
Generalize results – only if the sample is representative of the population
Probability sampling
Non-probability sampling
2
Probability sampling –
Random Sampling
Each member of the population has an equal chance of being selected.
3
Probability sampling –
Stratified Random Sampling
Take equal samples from each group (layers, strata).
4
Probability sampling –
Proportional Stratified Sampling
Take equal proportions of samples from each group (layers, strata).
5
Probability sampling –
Cluster Sampling
Take equal proportions of samples from certain regions only.
6
Non-probability Sampling –
Convenience Sampling
No attempt to have a representative sample
Examples:
Survey people in your neighborhood.
Customer satisfaction cards in a restaurant.
Survey all companies who have had projects done by NWMOC.
Survey all Human Resources Managers at Stout Career Fair.
7
Sample size?
Entire population, if N<100
20-50% of population, if 100 < N < 2000
About 400, if N > 2000
Affects the time and cost of the study, the precision of statistical results
Be sure to consider the response rate
8
Sampling Bias
Bias – an influence, condition, or set of conditions which distort the data
Sampling bias – is the sample random?
Examples:
Political polls by phone interview
A mail survey of alumni satisfaction, with 30% response rate
9
10
Dilbert
Click to edit Master text styles
Second level
Third level
Fourth level
Fifth level
Quantitative Methods/Confidence Intervals.pptx
Confidence Intervals
Some adapted from http://stattrek.com/estimation/confidence-interval.aspx and http://www.stat.yale.edu/Courses/1997-98/101/confint.htm
1
Confidence Interval
Statisticians use a confidence interval to describe the amount of uncertainty associated with a sample estimate of a population parameter.
It gives an estimated range of values which is likely to include an unknown population parameter,
the estimated range is calculated from a set of sample data.
Confidence Interval
Gives the probability that the interval produced by the sample method includes the true value of the parameter
You must assume a normal distribution
Confidence Interval Selection
Common choices for the confidence level are 0.90, 0.95, and 0.99. These levels correspond to percentages of the area of the normal density curve. For example, a 95% confidence interval covers 95% of the normal curve --
Normal Distribution
Confidence Intervals
Supp ...
The following calendar-year information is taken from the December.docx
The following calendar-year information is taken from the December 31, 2011, adjusted trial balance and other records of Azalea Company.
1. Each team member is to be responsible for computing one of the following amounts. You are not to duplicate your teammates' work. Get any necessary amounts from teammates. Each member is to explain the computation to the team in preparation for reporting to class.
a. Materials used.
b. Factory overhead.
c. Total manufacturing costs.
d. Total cost of goods in process.
e. Cost of goods manufactured.
2. Check your cost of goods manufactured with the instructor. If it is correct, proceed to part (3).
3. Each team member is to be responsible for computing one of the following amounts. You are not to duplicate your teammates' work. Get any necessary amounts from teammates. Each member is to explain the computation to the team in preparation for reporting to class.
a. Net sales.
b. Cost of goods sold.
c. Gross profit.
d. Total operating expenses.
e. Net income or loss before taxes.
CALCULATE T TEST
Calculate the “t” value for independent groups for the following data using the formula provided in the attached word document. Using the raw measurement data presented, determine whether or not there exists a statistically significant difference between the salaries of female and male human resource managers using the appropriate t-test. Develop a testable hypothesis, confidence level, and degrees of freedom. Report the required “t” critical values based on the degrees of freedom. Show calculations.
Answer
The null hypothesis tested is
H0: There is no significant difference between the average salaries of female and male human resource managers. (µ1= µ2)
The alternative hypothesis is
H1: There is significant difference between the average salaries of female and male human resource managers. (µ1≠ µ2)
The test statistic used is
12
12
2
~
NN
DM
MM
tt
S
+-
-
=
Where
22
1122
1212
(1)(1)
11
2
DM
NsNs
S
NNNN
éùéù
-+-
=+
êúêú
+-
ëûëû
Here M1 = 62,200, M2 = 63,700
s1 = 9330.95, s2 = 6912.95
N1 = 10, N2 = 10 (See the excel sheet)
Then,
(
)
(
)
22
(101)9330.95(101)6912.95
11
101021010
DM
S
éù
-+-
éù
=+
êú
êú
+-
ëû
êú
ëû
= 3672.267768
Therefore test statistic,
62,20063,700
3672.267768
t
-
=
= -0.408466946
Degrees of freedom = N1 + N2 – 2 = 10 + 10 – 2 = 18
Let the significance level be 0.05.
Rejection criteria: Reject the null hypothesis, if the calculated value of t is greater than the critical value of t at 0.05 significance level.
The critical values can be obtained from the student’s t tables with 18 d.f. at 0.05 significance level.
Upper critical value = 2.1
Lower critical value = -2.1
0
.
4
0
.
3
0
.
2
0
.
1
0
.
0
X
D
e
n
s
i
t
y
-
2
.
1
0
0
.
0
2
5
2
.
1
0
0
.
0
2
5
0
D
i
s
t
r
i
b
u
t
i
o
n
P
l
o
t
T
,
d
f
=
1
8
Conclusion: Fails to reject the null hypothesis. The sample does not provide enough evidence to support the claim that there is significant difference ...
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