Chapter 10: Hypothesis Tests
Copyright © 2016 Pearson Education, Inc.
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Chapter 10 – Hypothesis Tests
Regarding a Parameter
OUTLINE
10.1 The Language of Hypothesis Testing
10.2 Hypothesis Tests for a Population
Proportion
10.3 Hypothesis Tests for a Population Mean
10.4 Putting It Together: Which Procedure
Do I Use?
Putting It Together
In Chapter 9, we mentioned there are two types of inferential
statistics:
(1) estimation
(2) hypothesis testing
We have already discussed procedures for estimating the
population proportion and the population mean.
We now focus our attention on hypothesis testing. Hypothesis
testing is used to test statements regarding a characteristic of one
or more populations. In this chapter, we will test hypotheses
regarding a single population parameter, including the population
proportion and the population mean.
Chapter 10: Hypothesis Tests
Copyright © 2016 Pearson Education, Inc.
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Section 10.1
The Language of Hypothesis Testing
Objectives
Answer the following after watching the video.
After determining that the first five tosses are all tails is unlikely, what are the two possible conclusions that can be
drawn?
What does the video call “The Heart of Hypothesis Testing”?
We make an ______________________________ about reality.
We then look at (or gather) ____________________________________ to determine whether it contradicts our
assumption.
Objective 1: Determine the Null and Alternative Hypotheses
Answer the following after watching the video.
What is a hypothesis?
Why do we test statements about a population parameter using sample data?
State the definition of hypothesis testing.
Chapter 10: Hypothesis Tests
Copyright © 2016 Pearson Education, Inc.
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List the 3 steps in hypothesis testing.
1. Make a statement regarding the nature of the_______________________________.
2. Collect evidence (_____________________________) to test the statement.
3. Analyze the data to assess the ___________________________ of the statement.
State the definition of the two statements we’re looking to test (“hypotheses”):
The null hypothesis, denoted _________, is a statement to be tested. The null hypothesis is a statement of
______________________, ________________________ or __________________________ and is assumed
______________ until evidence indicates otherwise.
The alternative hypothesis, denoted ________, is a statement that we are trying to find evidence to
____________________.
List the three ways to set up the null and alternative hypotheses.
1. Equal versus not equal hypothesis (____________________ test)
H0: parameter = some value
H1: parameter some value (fill in the circle with the correct inequality symbol)
2. Equal versus less than (____________________ test)
H0: parameter = some value
H1: parameter some value (fill in the circle with the correct inequality symbol)
3. Equal versus greater than (____________________ test)
H0: parameter = some value
H1: parameter some value (fill in the circle with the correct inequality symbol)
Left- and right-tailed tests are referred to as _______________________________. Notice that in the left-tailed test, the
direction of the inequality sign in the alternative hypothesis points to the __________________ (<), whereas in the right–
tailed test, the direction of the inequality sign in the alternative hypothesis points to the ____________________ (>). In
all three tests, the _________________ hypothesis contains a statement of equality.
Chapter 10: Hypothesis Tests
Copyright © 2016 Pearson Education, Inc.
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Example 1 Forming Hypotheses
For each situation, determine the null and alternative hypotheses. State whether the test is two-tailed, left-tailed, or right-
tailed.
A) The Medco pharmaceutical company has just developed a new antibiotic for children. Two percent of children taking
competing antibiotics experience headaches as a side effect. A researcher for the Food and Drug Administration wants to
know if the percentage of children taking the new antibiotic and experiencing headaches as a side effect is more than 2%.
B) The Blue Book value of a used three-year-old Chevy Corvette Z06 is $56,130. Grant wonders if the mean price of a
used three-year-old Chevy Corvette Z06 in the Miami metropolitan area is different from $56,130.
C) The standard deviation of the contents in a 64-ounce bottle of detergent using an old filling machine is 0.23 ounce.
The manufacturer wants to know if a new filling machine has less variability.
Objective 2: Explain Type I and Type II Errors
Four Possible Outcomes From Hypothesis Testing
1. Reject the null hypothesis when the alternative hypothesis is true. This decision would be correct.
2. Do not reject the null hypothesis when the null hypothesis is true. This decision would be correct.
3. ___________________________________________________________________________________.
This decision would be incorrect. This type of error is called a Type I error.
4. ___________________________________________________________________________________.
This decision would be incorrect. This type of error is called a Type II error.
Chapter 10: Hypothesis Tests
Example 2 Type I and Type II Errors
The Medco pharmaceutical company has just developed a new antibiotic. Two percent of children taking competing
antibiotics experience headaches as a side effect. A researcher for the Food and Drug Administration wishes to know if
the percentage of children taking the new antibiotic who experience a headache as a side effect is more than 2%.
The researcher conducts a hypothesis test with H0: p = 0.02 and H1: p > 0.02.
Explain what it would mean to make a (A) Type I error and (B) Type II error.
Commonplace notation for the probability of making a Type I error and the probability of making a Type II error: