### Chapter 9 Hypothesis Testing

```Chapter 9
Hypothesis Testing
9.1
The Language of Hypothesis
Testing
Example: Illustrating Hypothesis
Testing
• According to the National Center for
Chronic Disease Prevention and Health
Promotion, 73.8% of females between the
ages of 18 and 29 years exercise. Kathleen
believes that more women between the ages
of 18 and 29 years are now exercising.
How to test her claim?
• Ask all females in the U.S.A? It’s
impossible!!
• Take a random sample, for example, survey
1000 woman between 18 and 29 years old.
And then make a statistical inference about
the population---all females.
Statistical Inference
• She obtains a simple random sample of 1000
women between the ages of 18 and 29 years and
finds that 750 of them are exercising.
• Is this evidence that the percent of women
between the ages of 18 and 29 years who are
exercising has increased? Or how likely is it to
obtain a sample of 750 out of 1000 women
exercising from a population when the percentage
of women who exercise is 73.8%?
• What if Kathleen’s sample resulted in 920 women
exercising?
• If the actual percentage of women who exercise is
73.8%, the likelihood of obtaining a sample of 920
women who exercise is extremely low. Therefore ,
the actual percentage of women who exercise is
indeed bigger than 73.8%---that is ,the sample
support Kathleen’s claim-or Hypothesis.
Steps in Hypothesis Testing
2. Evidence (sample data) is collected
in order to test the claim.
3. The data is analyzed in order to support
or refute the claim.
A hypothesis is a statement or claim
regarding a characteristic of one or more
populations.
In this chapter, we look at hypotheses
regarding a single population.
Examples of Claims Regarding a Characteristic
of a Single Population
• In 1997, 43% of Americans 18 years or older
participated in some form of charity work. A researcher
believes that this percentage different today.
H0 : p=43%
H1: p

43%
Examples of Claims Regarding a Characteristic
of a Single Population
• In 1997, 43% of Americans 18 years or older
participated in some form of charity work. A researcher
believes that this percentage different today.
• In June, 2001 the mean length of a phone call on a
cellular telephone was 2.62 minutes. A researcher
believes that the mean length of a call has increased
since then.
Examples of Claims Regarding a Characteristic
of a Single Population
• In 1997, 43% of Americans 18 years or older
participated in some form of charity work. A researcher
believes that this percentage different today.
• In June, 2001 the mean length of a phone call on a
cellular telephone was 2.62 minutes. A researcher
believes that the mean length of a call has increased
since then.
• Using an old manufacturing process, the standard
deviation of the amount of wine put in a bottle was 0.23
ounces. With new equipment, the quality control
manager believes the standard deviation has
decreased.
CAUTION!
We test these types of claims using
sample data because it is usually
impossible or impractical to gain access
to the entire population. If population data
is available, then inferential statistics is
not necessary.
Consider the researcher who believes that the
mean length of a cell phone call has increased
from its June, 2001 mean of 2.62 minutes.
To test this claim, the researcher might obtain a
simple random sample of 36 cell phone calls.
Suppose he determines the mean length of the
phone call is 2.70 minutes. Is this enough
evidence to conclude the length of a phone call
has increased?
We will assume the length of the phone call is still
2.62 minutes. Assume the standard deviation
length of a phone call is known to be 0.78 minutes.
What if our sample resulted in a sample
mean of 2.95 minutes?
Hypothesis testing is a procedure, based
on sample evidence and probability, used to
test claims regarding a characteristic of one
or more populations.
The null hypothesis, denoted Ho (read “Hnaught”), is a statement to be tested. The null
hypothesis is assumed true until evidence
indicates otherwise. In this chapter, it will be a
statement regarding the value of a population
parameter.
The alternative hypothesis, denoted, H1 (read
“H-one”), is a claim to be tested. We are trying to
find evidence for the alternative hypothesis. In
this chapter, it will be a claim regarding the value
of a population parameter.
In this chapter, there are three ways to set up the
null and alternative hypothesis.
1. Equal versus not equal hypothesis (two-tailed
test)
Ho: parameter = some value
H1: parameter ≠ some value
In this chapter, there are three ways to set up the
null and alternative hypothesis.
1. Equal versus not equal hypothesis (two-tailed
test)
Ho: parameter = some value
H1: parameter ≠some value
2. Equal versus less than (left-tailed test)
Ho: parameter = some value
H1: parameter < some value
In this chapter, there are three ways to set up the
null and alternative hypothesis.
1. Equal versus not equal hypothesis (two-tailed
test)
Ho: parameter = some value
H1: parameter ≠ some value
2. Equal versus less than (left-tailed test)
Ho: parameter = some value
H1: parameter < some value
3. Equal versus greater than (right-tailed test)
Ho: parameter = some value
H1: parameter > some value
The null hypothesis is a statement of
“status quo” or “no difference” and always
contains a statement of equality. The null
hypothesis is assumed to be true until we
have evidence to the contrary. The claim
that we seek evidence for always
becomes the alternative hypothesis.
EXAMPLE Forming Hypotheses
For each of the following claims, determine the null
and alternative hypothesis.
• In 1997, 43% of Americans 18 years or older participated
in some form of charity work. A researcher believes that
this percentage different today.
• In June, 2001 the mean length of a phone call on a
cellular telephone was 2.62 minutes. A researcher
believes that the mean length of a call has increased
since then.
• Using an old manufacturing process, the standard
deviation of the amount of wine put in a bottle was 0.23
ounces. With new equipment, the quality control manager
believes the standard deviation has decreased.
Four Outcomes from Hypothesis Testing
1. We could reject Ho when in fact H1 is true. This
would be a correct decision.
Four Outcomes from Hypothesis Testing
1. We could reject Ho when in fact H1 is true. This
would be a correct decision.
2. We could not reject Ho when in fact Ho is true.
This would be a correct decision.
Four Outcomes from Hypothesis Testing
1. We could reject Ho when in fact H1 is true. This
would be a correct decision.
2. We could not reject Ho when in fact Ho is true.
This would be a correct decision.
3. We could reject Ho when in fact Ho is true. This
would be an incorrect decision. This type of error
is called a Type I error.
Four Outcomes from Hypothesis Testing
1. We could reject Ho when in fact H1 is true. This
would be a correct decision.
2. We could not reject Ho when in fact Ho is true.
This would be a correct decision.
3. We could reject Ho when in fact Ho is true. This
would be an incorrect decision. This type of error
is called a Type I error.
4. We could not reject Ho when in fact H1 is true.
This would be an incorrect decision. This type of
error is called a Type II error.
EXAMPLE
Type I and Type II Errors
For each of the following claims explain what it
would mean to make a Type I error. What would it
mean to make a Type II error?
• In 1997, 43% of Americans 18 years or older
participated in some form of charity work. A
researcher believes that this percentage different
today.
• In June, 2001 the mean length of a phone call on
a cellular telephone was 2.62 minutes. A
researcher believes that the mean length of a call
has increased since then.
As the probability of a Type I error
increases, the probability of a Type II
error decreases, and vice-versa.
CAUTION!
EXAMPLE
Wording the Conclusion
In June, 2001 the mean length of a phone call on a
cellular telephone was 2.62 minutes. A researcher
believes that the mean length of a call has
increased since then.
(a) Suppose the sample evidence indicates that
the null hypothesis should be rejected. State the
wording of the conclusion.
(b) Suppose the sample evidence indicates that
the null hypothesis should not be rejected. State
the wording of the conclusion.
```