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Doing Statistics for Business
Data, Inference, and Decision Making
Chapter 8
Hypothesis
Testing :
An Introduction
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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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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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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
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the stated problem.
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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 p value is defined to be the smallest
value of  for which you can reject H0.
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TRY IT NOW!
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 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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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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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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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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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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Figure 8.3 Rejection Region for a two-tail test
of m with  = 0.05
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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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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
base your decision.
 In doing any hypothesis test there are two possible
errors you can make
Type I and
Type II
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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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