Car Sales Statistics

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```					Doing Statistics for Business
Data, Inference, and Decision Making
Marilyn K. Pelosi
Theresa M. Sandifer

Chapter 8
Hypothesis
Testing :
An Introduction

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Doing Statistics for Business
Chapter 8 Objectives

 What Is a Hypothesis Test?
 Overview of Hypotheses to be Tested
 The Pieces of a Hypothesis Test
 Two-Tail Tests of the Mean: Large Sample
 Which Theory Should Go into the Null
Hypothesis?
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Chapter 8 Objectives (con’t)

 One-Tail Tests of the Mean: Large Sample
 What Error Could You be Making?

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What is an Hypothesis Test?
The word hypothesis has the same meaning in
statistics as it does in everyday use. What does this
word mean to you? Some possibilities are:
 an idea
 an assumption
 a guess
 a theory
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In statistics, a Hypothesis is an idea, an
assumption, or a theory about
the characteristics of one or more populations.

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A Hypothesis Test is a statistical procedure
that involves formulating a hypothesis and
using sample data to decide on the validity of
the hypothesis.

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7-11 Stores Possible Hypotheses
7-11 stores are located all over the Northeast. Management is
studying sales data. Develop a specific hypothesis for each of the
different types of hypotheses that we have discussed. Here’s one
hypothesis to get you started:
Type of Hypothesis                                Specific Hypothesis
The shape of the distribution of the variable     Daily sales at Store 23 are
in one population                                 normally distributed

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The Sports Complex
Possible Hypotheses
A particular university is considering building a new sports
complex. It wishes to know if the sports complex would be widely used
by students. Develop a specific hypothesis for each of the different types
of hypotheses that we have discussed.

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The Null Hypothesis is a statement about
a parameter of the population(s).
It is referred to as H0.
The Alternative Hypothesis is a statement
about a parameter of the population(s) that
is opposite to the null hypothesis.
It is referred to as HA.

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The Potato Chip Manufacturer
Setting Up the Null and Alternative
Hypotheses
Many people eat chips with their soda. Suppose a potato chip
manufacturer is concerned that the bagging equipment may not be
functioning properly when filling 10-oz bags. You have been asked to
set up a hypothesis test that will help determine if there is a problem with
the bagging equipment. What null and alternative hypothesis would you
use?
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Discovery Exercise 8.1
Formulating Hypotheses
Consider the population of all M & M packages like the
one you have in your hand.
Step 1: Identify as many different variables as you can. Be sure you have
some quantitative and some qualitative variables. Record the values of
these variables for your package. (Hint: You should carefully examine the
package before you rip it open.)

Step2: Select one of the quantitative variables and set up a null and
alternative hypothesis for a parameter of this variable.
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Doing Statistics for Business
Discovery Exercise 8.1
Formulating Hypotheses (con’t)
Step 3: Select one of the qualitative variables and set up
a null and alternative hypothesis for a parameter of this variable.

Step 4: As a class agree on several quantitative and qualitative variables
that you feel are important. Record the data for all of the teams on each
of these variables.

Step 5: Use the tools of descriptive statistics to display these data.
Step 6: Enjoy the M&M’s!
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A Test Statistic is calculated from
the sample data and is used to
decide between the null and
alternative hypothesis.

The rejection region is the range
of values of the test statistic that will
lead you to reject the null hypothesis.
Alpha,  , is the area of the rejection
region.
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5-Step Hypothesis Testing Procedure
Step 1: Set up the null and alternative hypotheses.
Step 2: Define the test procedure. This includes selecting
the right test, picking the value of , and finding the
rejection region.
Step 3: Collect the data and calculate the test statistic.
Step 4: Decide whether or not to reject the null
hypothesis.
Step 5: Interpret the statistical decision in terms of
the stated problem.                                14
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Figure 8.1 Possible Rejection
Region

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Figure 8.2 Rejection Region for a
two-tail test of m

-z /2   z /2

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The Tissue Company
Finding the Rejection Region

Suppose the tissue company decided to set  at 0.10.
Find the rejection region.

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Discovery Exercise 8.2
Exploring the Impact of Varying
the Value of 
You may remember that in Chapter 4 we examined the data collected by a
company that was concerned about the length of time its customers were
on hold. The data shown below were first presented to you in Example
4.15 in your textbook. There are 50 observations on customer hold times:
0.6   4.6   5.6   6.3   6.8   7.5   7.8   8.3   8.9    9.6
2.9   4.7   6.0   6.3   6.9   7.5   7.9   8.4   9.2   10.1
3.4   5.2   6.0   6.6   6.9   7.6   8.0   8.4   9.2   10.2
3.8   5.5   6.1   6.6   7.0   7.6   8.1   8.6   9.4   10.7
4.5   5.5   6.1   6.7   7.2   7.8   8.2   8.6   9.4   11.1

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Discovery Exercise 8.2
Exploring the Impact of Varying
the Value of  (con’t)
The company wishes to test the hypothesis that the true mean hold time is
7 minutes. The standard deviation of hold times is known to be 2 minutes.
(a) Test this hypothesis using a value of  = 0.10.
(b) Now vary the value of  and complete the following table.
                          Rejection Region         Decision
0.10 (from part a above)
0.05
0.02
0.01
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Discovery Exercise 8.2
Exploring the Impact of Varying
the Value of  (con’t)
( c) What happened to your decision as the value of  changed?

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The p value is defined to be the smallest
value of  for which you can reject H0.

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The Tissue Company
Finding the p Value
Find the p value for the tissue company’s two-tail test of m.
Recall that the average MDStrength was found to be 980 lb/ream
and the Z statistic was calculated to be -2.40.

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A Type I Error is made when you reject the
null hypothesis and the null hypothesis is
actually true. In other words, you incorrectly
reject a true null hypothesis.
A Type II Error is made when you fail to reject
the null hypothesis and the null hypothesis is
false. In other words, you continue to believe a
false null hypothesis.
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The Potato Chip Manufacturer
Examining the Type I and Type II Errors

Find the Type I and Type II errors for the hypothesis test that you set up
for the potato chip manufacturer of this chapter.

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The probability of making a Type I Error is
called  (alpha).

The probability of making a Type II Error is
called  (beta).

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New Package Design
Setting the Value of 
We have seen that a one-sided test is often used to investigate
whether a new method of advertising or producing something is better
than the existing method. Consider a company that is trying a new
package design for its product. The average sales for this product are
currently \$1500/month. The null and alternative hypotheses would be
H0.: m  \$1500
HA.: m > \$1500
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New Package Design
Setting the Value of  (con’t)

In terms of the company’s decision to adopt or not adopt this new
design, what are the Type I and Type II errors?

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A Two-Tail Test of the population mean has
the following null and alternative hypotheses:

H0: m = [a specific number]
HA: m  [a specific number]

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The Chapperel Steel Company
Setting Up the Null and Alternative
Hypotheses for a Two-Tail Test of the Mean
Another recent management approach is to have employees become actual
partners of the business. Chapperel Steel Company has done exactly this
and the company feels that one of the benefits of this concept is that the
average number of sick days will decrease. Prior to implementing this
program, Chapperel had an average of 7.2 sick days per employee. Set up
the null and alternative hypothesis to test if the average number of sick
days per employee is different from 7.2.
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A Lower-Tail Test of the population mean has
the following null and alternative hypotheses:

H0: m  [a specific number]
HA: m < [a specific number]

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The Bank Example
Lower-Tail Test
Suppose a bank knows that their customers are waiting in line an average
of 10.2 minutes during the lunch hour. The branch manager has decided
to add an additional teller during the 12-2 p.m. period and wishes to test
the hypothesis that the average wait has decreased due to the additional
teller. Set up the null and alternative hypothesis for the bank manager.

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An Upper-Tail Test of the population mean
has the following null and alternative hypotheses:

H0: m  [a specific number]
HA: m > [a specific number]

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Setting Up an Upper-Tail Test
Suppose a company has implemented a new advertising program
in the hope of increasing sales from last year’s annual average of \$4.3
million. Set up the null and alternative hypotheses to test the theory that
sales have increased.

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Summary            A Two-Tail Test
 Is used to test if the parameter has shifted away
from a certain number in either direction,
increased or decreased.
 Must always be set up so the “=“ theory is the null
hypothesis.
 Is used when the problem statement has the key
words changed or different in the problem
statement.
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Summary             A Lower-Tail Test
 Is used to test if the parameter has shifted to a
number less than a certain number.
 Must always be set up so the “=“ as part of the
null hypothesis.
 Is used when the problem statement has the key
words decreased, reduced, less than.
 The theory that you wish to “prove” is placed into
the alternative hypothesis.
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Summary             An Upper-Tail Test
 Is used to test if the parameter has shifted to a
number more than a certain number.
 Must always be set up so the “=“ as part of the
null hypothesis.
 Is used when the problem statement has the key
words increased, greater than.
 The theory that you wish to “prove” is placed into
the alternative hypothesis.
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Judicial System
Setting Up the Null and Alternative
Hypothesis

If you think about the judicial system in terms of a hypothesis test, how
would you set up the null and the alternative hypotheses?

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VCR Manufacturer
Setting Up the Hypotheses So the Status
Quo Is in the Null Hypothesis

Suppose a manufacturer of VCRs claims that the average life of his VCRs
is at least three years. You have a VCR made by this company and have
had problems with it, and so you question this claim. Set up the
hypothesis test to investigate the manufacturers claims.

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Finding the Rejection Region

Try to predict what will happen to the -Z  value for the one-tail
test if  = 0.025. Now find it to confirm your guess.

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Frozen Foods
Lower-Tail Test of the Mean
Jake Bramhall can identify the make, model, and number of
cylinders of any passing car but he can’t tell the difference between
stewed tomatoes and tomato paste. While more men are pushing shopping
carts these days, many like Mr.. Bramhall show little aptitude in the
supermarket and display markedly different purchasing behavior than
women.
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Frozen Foods
Lower-Tail Test of the Mean (con’t)
A study done by Consumer Network Inc. shows that the average
amount of money spent by 100 single men on facial tissues was \$7.38.
On the basis of these data can you conclude that men spend less money on
facial tissues than the average \$8.19 spent by women on facial tissues?
Use a population standard deviation of \$3.50 and  value of 0.05. Are the
results different if you use  = 0.01?
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Supermarket Survey
Upper-Tail Test of the Mean
From the same supermarket survey it is found that the 100 men
spent, on on the average, \$19.98 on low-calorie soft drinks. Is there
enough evidence to conclude that men spend more than women, who, on
the average, spent \$18.86? Assume that the population standard deviation
is \$10 and use  = 0.05.

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Figure 8.3 Rejection Region for a two-tail test
of m with  = 0.05
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Doing Statistics for Business
Chapter 8 Summary
In this chapter you have learned:
 The key steps in doing any Hypothesis Test begins
with formulating two opposing viewpoints called
the Null and Alternative Hypotheses.
 These hypotheses are theories or ideas about the
value of one or more population parameters.
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Doing Statistics for Business
Chapter 8 Summary (con’t)
 The technique of Hypothesis Testing helps you
decide between these opposing hypotheses using
the sample data as the evidence upon which to
 In doing any hypothesis test there are two possible
errors you can make
Type I and
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Type II
Doing Statistics for Business
Chapter 8 Summary (con’t)
 The probability of making these errors are labeled
 and , respectively.
 Large Sample Tests are applied whenever you
know the population standard deviation or if you
have a sufficiently large sample size, n > 30.

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