PAGE O&M Statistics – Inferential Statistics: Hypothesis Testing Inferential Statistics Hypothesis testing Introduction In this week, we transition from confidence intervals and interval estimates to hypothesis testing, the basis for inferential statistics. Inferential statistics means using a sample to draw a conclusion about an entire population. A test of hypothesis is a procedure to determine whether sample data provide sufficient evidence to support a position about a population. This position or claim is called the alternative or research hypothesis. “It is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” (Mason & Lind, pg. 336). This Week in Relation to the Course Hypothesis testing is at the heart of research. In this week, we examine and practice a procedure to perform tests of hypotheses comparing a sample mean to a population mean and a test of hypotheses comparing two sample means. The Five-Step Procedure for Hypothesis Testing (you need to show all 5 steps – these contain the same information you would find in a research paper – allows others to see how you arrived at your conclusion and provides a basis for subsequent research). Step 1 State the null hypothesis – equating the population parameter to a specification. The null hypothesis is always one of status quo or no difference. We call the null hypothesis H0 (H sub zero). It is the hypothesis that contains an equality. State the alternate hypothesis – The alternate is represented as H1 or HA (H sub one or H sub A). The alternate hypothesis is the exact opposite of the null hypothesis and represents the conclusion supported if the null is rejected. The alternate will not contain an equal sign of the population parameter. Most of the time, researchers construct tests of hypothesis with the anticipation that the null hypothesis will be rejected. Step 2 Select a level of significance (α) which will be used when finding critical value(s). The level you choose (alpha) indicates how confident we wish to be when making the decision. For example, a .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong (what is called the likelihood of committing a Type 1 error). The level of significance is set by the individual performing the test. Common significance levels are .01, .05, and .10. It is important to always state what the chosen level of significance is. Step 3 Identify the test statistic – this is the formula you use given the data in the scenario. Simply put, the test statistic may be a Z statistic, a t statistic, or some other distribution. Selection of the correct test statistic will depend on the nature of the data being tested (sample size, whether the population standard deviation is known, whether the data is known to be normally distributed). The sampling distribution of the test statistic is divided into t.

1. PAGE
O&M Statistics – Inferential Statistics: Hypothesis Testing
Inferential Statistics
Hypothesis testing
Introduction
In this week, we transition from confidence intervals and
interval estimates to hypothesis testing, the basis for inferential
statistics. Inferential statistics means using a sample to draw a
conclusion about an entire population. A test of hypothesis is a
procedure to determine whether sample data provide sufficient
evidence to support a position about a population. This position
or claim is called the alternative or research hypothesis.
“It is a procedure based on sample evidence and probability
theory to determine whether the hypothesis is a reasonable
statement” (Mason & Lind, pg. 336).
This Week in Relation to the Course
Hypothesis testing is at the heart of research. In this week, we
examine and practice a procedure to perform tests of hypotheses
comparing a sample mean to a population mean and a test of
hypotheses comparing two sample means.
The Five-Step Procedure for Hypothesis Testing (you need to
show all 5 steps – these contain the same information you would
find in a research paper – allows others to see how you arrived
at your conclusion and provides a basis for subsequent
research).
Step 1

2. State the null hypothesis – equating the population parameter to
a specification. The null hypothesis is always one of status quo
or no difference. We call the null hypothesis H0 (H sub zero). It
is the hypothesis that contains an equality.
State the alternate hypothesis – The alternate is represented as
H1 or HA (H sub one or H sub A). The alternate hypothesis is
the exact opposite of the null hypothesis and represents the
conclusion supported if the null is rejected. The alternate will
not contain an equal sign of the population parameter.
Most of the time, researchers construct tests of hypothesis with
the anticipation that the null hypothesis will be rejected.
Step 2
Select a level of significance (α) which will be used when
finding critical value(s).
The level you choose (alpha) indicates how confident we wish
to be when making the decision.
For example, a .05 alpha level means that we are 95% sure of
the reliability of our findings, but there is still a 5% chance of
being wrong (what is called the likelihood of committing a Type
1 error).
The level of significance is set by the individual performing the
test. Common significance levels are .01, .05, and .10. It is
important to always state what the chosen level of significance
is.
Step 3
Identify the test statistic – this is the formula you use given the

3. data in the scenario. Simply put, the test statistic may be a Z
statistic, a t statistic, or some other distribution. Selection of
the correct test statistic will depend on the nature of the data
being tested (sample size, whether the population standard
deviation is known, whether the data is known to be normally
distributed).
The sampling distribution of the test statistic is divided into two
regions, a region of rejection called the critical region and the
non-rejection region. The rejection region lies in the tails of the
curve starting at the critical value of the test statistic. The test
statistic is the value calculated by using the appropriate
sampling distribution. The critical values are tabulated values
found in statistical tables on the rEsource page. If the test
statistic falls into the region of nonrejection, then the null
hypothesis is not rejected. If the test statistic falls into the
rejection region, the null hypothesis is rejected.
Step 4
State the decision rule.
The decision to reject the null hypothesis is made when the
value of the test statistic exceeds the critical value.
Step 5
Take a sample and arrive at a decision.
Our job now is to calculate the value of Z (or t or other
distribution) based on a sample. If the calculated value of Z is
larger than the critical Z value, the Z value separating the
rejection region from the nonrejection region, then we will
reject the null hypothesis in favor of the alternate. On the other
hand, if the calculated value of Z is smaller than the critical
value that would indicate the observed result was probably due

4. to chance rather than effect. When the null hypothesis is
rejected, the results are considered to be statistically
significant. The observed results are not due to the chance of
drawing a biased sample. When the null hypothesis is not
rejected, the results are considered to be not statistically
significant. Random chance was at work.
One-Sample (Large Sample) Hypothesis Test
Let’s say a drug company wants to show that its new drug,
Releeva, provides pain relief faster than the 30 minutes its well-
established competitor, No-ache, advertises. The Releeva team
issues the drug to 100 people in a pain relief clinic and records
the time to relief reported by the patients. The researchers
record each person’s reported time it took for their pain to
disappear and found that the average time was 26.2 minutes
with a standard deviation of 8 minutes.
So, the question is, did we get a sample mean of 28.2 minutes
just because we randomly chose a sample of 100 from a
population where the true mean is 30 minutes, or does our
sample give enough evidence to conclude that the true mean is
really less than 30 minutes?
Step 1
The null hypothesis, or status quo is that the mean time to relief
is 30 minutes (or more). If the data causes us to reject this
hypothesis, then the alternate (which supports our position)
must be true. The alternate hypothesis is that the mean time to
relief is less than 30 minutes. In symbols, it would look like
this:
Ho: μ = 30.
Ha: u < 30.
Note that the equal sign is in the null hypothesis. Also, this is a

5. “one-tail test” because the alternate hypothesis only tests one
side of the normal curve. HAD THE QUESTION ASKED IF
RELEEVA HAD A MEAN TIME TO RELIEF OF EXACTLY 30
MINUTES, THE TEST WOULD HAVE BEEN:
Ho: μ = 30.
Ha: u < > 30
In this “two-tailed test” the alternate hypothesis looks to both
tails of the distribution because rejecting the null hypothesis
means the time to relief is either less than 30 minutes or more
than 30 minutes.
Step 2
We decide that we want to be 95% confident in our answer, ά is
.05.
Step 3
This is called the “Decision Rule” (is Step 4 in your text – I like
to switch steps 3 and 4 – seem to make more sense to me). So,
the DR is: Reject the null if the computed number of standard
errors between the hypothesized population mean of 30 minutes
and the sample mean of 28.2 minutes is greater than 1.65.
(Since this is a large sample (> 30) we can use Appendix D.
With a one-tailed test we subtract the .05 level of significance
from .5000 (the table works from the middle of the curve) – this
gives us an area under that half of the curve of .4500. Look this
up in the “heart” of the table (working our way backwards
through the table) and we don’t find .4500 but we do find .4495
(z = 1.64) and .4505 (z = 1.65). We can round up and choose
1.65.)
If the calculated value of Z is larger than 1.65, then the result
will fall in the rejection region (the tail of the distribution), and

6. we will reject the null hypothesis in favor of the alternate. This
would indicate that Releeva is faster and that the observed
results are probably not due to the random chance that the
individuals selected for sampling were predisposed to a
favorable result. We would say there is statistically significant
evidence that the new drug works faster. On the other hand, if
the calculated value of Z is smaller than 1.645, that would
indicate that observed result was probably due to chance rather
than the efficacy of Releeva. The result in that case would be
deemed not statistically significant.
Step 4
This is where we calculate just how far apart are the
hypothesized population mean and the sample mean. We use
the following formula – you’ve seen this before but note that we
are using standard error (s/√n) rather than just standard
deviation (s):
z = X-bar – - 30 = 1.8 = 2.25
standard errors
s /√n 8//√100 .8
Step 5
This is where we state our conclusion and interpret it.
Our conclusion is that we will reject the null hypothesis -- the
sample mean is further than 1.65 standard errors from the
hypothesized population mean. This means that it is unlikely
that this sample came from a population that has a mean of 30
minutes. The probability of this is:

7. 2.25 standard errors equates to a probability of .4878. So, the
probability of this sample mean coming from a population
where 30 minutes is true is .5000 - .4878 = .0122 or 1.22% --
which is much less than the level of significance of .05 or 5%.
So the evidence leads us to believe that Releeva provides pain
relief faster than its competitor, No-ache. The reduction in time
is said to be “significant.”
Two-Sample (Independent Large Samples) Hypothesis Test
Clark Heter is an industrial engineer at Lyons Products. He
would like to determine whether there are more units produced
on the afternoon shift than on the day shift. A sample of 54
day-shift workers showed that the mean number of units
produced was 345, with a standard deviation of 21. A sample of
60 afternoon-shift workers showed that the mean number of
units produced was 351. with a standard deviation of 28 units.
At the .05 significance level, is the number of units produced on
the afternoon shift larger?
Step 1:
Null hypotheses: H0: u1 = u2 There is no significant
difference in between the population mean of the day shift, and
the population mean of the afternoon shift
Alternate hypotheses: H1: u1 < u2 The day shift population
is less than the afternoon shift population mean. Restated: The
afternoon shift population mean is greater than the day shift
population mean.
Step 2: The level of significance is .05 or 5%
Step 3: Decision Rule:
.50 - .05 = .45; .4500 = z of 1.65
Reject the null if the computed number of standard errors
between the two sample means is > 1.65
Step 4: Test Statistic:

8. Conclusion and interpretation: Fail to reject the null – there is
not enough evidence to conclude that these two samples came
from two different populations. There is only 1.3 standard
errors between them (much less than the critical value of 1.65),
so we conclude that there is not a significant difference in the
two shifts’ production.
The p-value = .5000 - .4032 = .0968 or 9.68% (more than the
level of significance of .05 or 5%)
Reference
Maon, R., Lind, D., Marchal, B. and Wathen, S, (2006). Basic
Statistics for Business and Economics (5th ed.). McGraw-Hill,
Irwn.
Page 1
Perceptual Map for [Product]
Positioning for [product]
[Name]
Positioning Presentation
MKT/421 WKe
Faculty: [Name]
*
*
Name

9. Name
Assignment:
You will develop and give a presentation on the marketing mix
of your current company using the “Record Presentation”
feature of Microsoft PowerPoint. In addition to submitting your
assignment for grading, you will post your assignment to a WK4
discussion thread for review and discussion with your
classmates.
For information about how to use the Microsoft PowerPoint
Record Slideshow featurehttps://support.office.com/en-
ZA/article/Record-your-slide-show-in-PowerPoint-2013-
9d136e4a-9717-49ad-876e-77aeca9c17eb
*
Perceptual Map for [Product]
Presentations need the same document elements as a paper,
including an introduction, conclusion, and header elements.Tips
for preparing a good introductionCapture your audience’s
attention with a “hook.”Indicate what the presentation is
about.Explain how you will approach the topic.Refer to the 5-
paragraph tutorial from Writing Wizards in the Tutorials &
Guides section of the Center for Writing Excellence for more
information about writing introductions.
Introduction
*
*
Name
Name
Perceptual Map for [Product]

10. Use this section to define the basic concepts you will cover in
the presentation to lay a foundation that will support your
analysis and recommendations. Key sources include:Chapter 9
of Kerin, Roger A., Hartley, Steven W., & Rudelius, W. (2015).
Marketing, 12th ed. McGraw-Hill Education. New York:
NY.Key concepts to explorePositioningCompetitive
analysisSWOT analysisPerceptual mappingMake sure you cite
your sources on your slides and in the Speaker’s NotesMeet
academic standardsEnhance the credibility of your analysis and
recommendations
Definitions
*
*
Name
Name
Perceptual Map for [Product]
Perceptual mappingDefine perceptual mapping.Explain the
process of perceptual mapping.Explain how you will apply this
process to create the perceptual map for your product.Identify
the two product attributes you will use to compare competing
products.Explain why you selected those attributes.List the key
competitors in the product category.Allocate scores for each
product using the attributes you selected.Cite your sources.
*
*
Name
Name
Perceptual Map for [Product]
[EXAMPLE: DELETE THIS SLIDE]

11. Perceptual map to reposition Milk Chug for adults
*
Age: Child or Adult
Nutrition: Low to high
Instructions:
Using the “Text Box” icon, place the name of each product
where customers perceive it in comparison to others
(Kerin, Hartley, & Rudelius, 2015, pg. 241-242; Dawar &
Bagga, 2015)
XYZ OJ
Red Bull
Kool Aid
Latte
Nesquik
Hershey’s
Milk Chug
Nestea
V8
Jim Beam
Muscle Milk
*
Name
Name
Adapted from:
Dawar, N., & Bagga, C. K. (2015). A Better Way to Map Brand
Strategy. Harvard Business Review, 93(6), 90-97.
Kerin, Roger A., Hartley, Steven W., & Rudelius, W. (2015).
Marketing, 12th ed. McGraw-Hill Education. New York: NY.
*
Perceptual Map for [Product]

12. Perceptual map for [product]
*
Attribute 1
Attribute 2
*
Name
Name
Adapted from:
Dawar, N., & Bagga, C. K. (2015). A Better Way to Map Brand
Strategy. Harvard Business Review, 93(6), 90-97.
Kerin, Roger A., Hartley, Steven W., & Rudelius, W. (2015).

13. Marketing, 12th ed. McGraw-Hill Education. New York: NY.
*
Perceptual Map for [Product]
AnalysisExplain the placement of each competitor.Based on
your analysis, make recommendations for positioning your
product using one of the approaches explained in Chapter 9 of
Kerrin, Hartley, & Rudelius (2015).Head-to-
headDifferentiationFrom your analysis, what is the positioning
statement that emerges?Tips:Kerrin, Hartley, & Rudelius
(2015), pg. 242 includes a sample analysis and perceptual map
that positions a chocolate milk product for adults. Use this as a
model for the analysis of your product.
*
*
Name
Name
Perceptual Map for [Product]
ConclusionConsider the conclusion like the closing argument in
a jury trial.Summarize key concepts as “proof” to support your
analysis and recommendations.Summarize what you have
intended to communicate in the presentation.Leave the audience
with a final thought or challenge.
*
*
Name
Name
Perceptual Map for [Product]

14. References citedUse at least 3 references to course material to
support your marketing concepts and recommendations. The
assignment provides two:Dawar, N., & Bagga, C. K. (2015). A
Better Way to Map Brand Strategy. Harvard Business
Review, 93(6), 90-97.Kerin, Roger A., Hartley, Steven W., &
Rudelius, W. (2015). Marketing, 12th ed. McGraw-Hill
Education. New York: NY.Cite the sources you used to get
information about the products you selected. Possible sources
include:Company websiteSWOT database in the libraryFor the
purposes of this and other assignments in the course, your client
(me) requires that you develop your deliverables using APA
style and attributionsYour organizations and clients will likely
have their own styles they require you to use; so, get in the
habit of learning and applying specific styles for each situation.
*
*
Name
Name
Perceptual Map for [Product]
Presentation tipsWhen you finish your slides, record your
presentation using the “Record Slide Show” feature under the
“Slide Show” tab.Record your slide show in
PowerPoint>Include your presentation script in the Speaker’s
Notes for each slide.To edit the Master Slide elements:View >
Master View > Slide MasterEdit the name, title, and background
elements as necessary.You’re welcome to apply your own
creative flare to the slides; but, focus on the content and
substance.don’t waste too much time on fluffAlways design
within the Microsoft framework; if you find yourself doing
things manually, you’re likely doing things wrongMake sure
you delete the instructions.
*

15. *
Name
Name