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PADM 7060 Quantitative Methods for
Public Administration
Unit 4 Chapters 11-12
Jerry Merwin
Meier, Brudney & Bohte
Part IV: Inferential Statistics
 Unit 4
 Chapter 11: Introduction to Inference
 Chapter 12: Hypothesis Testing
 Unit 5
 Chapter 13: Estimating Population
Proportions
 Chapter 14: Testing the Difference
Between Two Groups
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference
 Explain the difference between
descriptive statistics and inferential
statistics.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 2)
 What are the basic concepts and
definitions associated with inferential
statistics?





Population
Parameters
Sample
Random selection
Statistic
Meier, Brudney & Bohte :
Chapter 11 Introduction to Inference (Page 3)
 How important is random selection to
the concept of inference?
 What are the difference in parameters
and statistics?
 Symbols (See table 11.1)
 Calculations
 Mean?
 Standard deviation?
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 4)
 How do we estimate the population
mean? (177)
 What do we mean by sampling error?
 How can we reduce sampling error?
 Ideal sample size is n  30.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 5)
 How do we estimate the population
standard deviation? (see pages 178-179)
 Why do we calculate s with the
denominator n-1?
 How can we reduce sampling error?
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 6)
 What is the standard error of the
mean? (pages 179-180)
 How can we estimate the standard
error of the mean without taking
many samples?
 See the formula on page 181
 Also, note the explanation about using
the estimated standard deviation in the
computations.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 7)
 Let’s look at the example on page
180 regarding the Yukon police:
 The calculations for standard error of the
mean are on page 181
 Next, we will talk about how we can use
this information.
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 8)
 What is the “Student’s t distribution”
(a.k.a. the t distribution)
 Characteristics:




With n > = 30 normal distribution works
Resembles normal distribution but flatter
Differs for each sample size
Need to know the degrees of freedom (df)
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 9)
 What is a confidence limit?
 How is it calculated?
 See formula
 Using our example from Yukon:
 First look up the t values in table 3 on 446
(see book about why we use .025 and d.f. = 4)
 With the formula, we get
 15.6 + (1.7 x 2.78) = 20.3 for the upper limit
 15.6 – (1.7 x 2.78) = 10.9 for the lower limit
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 10)
 With this information, what does it
tell us about the confidence limit?
 15.6 + (1.7 x 2.78) = 20.3 for the upper
limit
 15.6 – (1.7 x 2.78) = 10.9 for the lower
limit
 We are 95% confident that…
Meier, Brudney & Bohte:
Chapter 11 Introduction to Inference (Page 11)
 Problems 11.2, 11.6 11.8
Meier, Brudney & Bohte :
Chapter 12 Hypothesis Testing
 How is hypothesis testing related to theory and
research? (Diagram courtesy of Dr. Nolan J. Argyle, from the text listed below)
David Nachmias & Chava Nachmias, Research Methods in the Social Sciences, 2nd ed. New York: St. Martins Press, 1981, p. 23.
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 2)
 What is a hypothesis?
 How is a hypothesis important to a
manager?
 Explain the null hypothesis?
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 3)
 What are the steps in hypothesis
testing?
 Formulate the hypothesis
 Collect the relevant data
 Evaluate the hypothesis in light of the
data
 Accept or reject the hypothesis
 Revise your decisions in light of the new
information
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 4)
 What is the primary type of
hypothesis testing we will do in
managerial situations?
 Hypothesis testing with samples!
 Example from Prudeville
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 5)
 Who can explain the concept of onetailed and two-tailed tests?
 When do we use the one-tailed test?
 Figure 12.1
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 6)
 What are the two types of errors we
can make testing a null hypothesis?
 Type 1
 Type 2
 How can we decrease type 1 errors?
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
(Page 7)
 How can we determine sample size?
 Consider:
 The amount of error that can be tolerated
 The confidence one wants to have in the
error estimate
 The standard deviation of the population
Meier, Brudney & Bohte:
Chapter 12 Hypothesis Testing
 Problems 12.2, 12.6
(Page 8)