Chapter 9 Hypothesis Testing

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Chapter 9Hypothesis Testing

• 9.1
• The Language of Hypothesis Testing

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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.

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How to test her claim?

• Ask all females in the U.S.A? Its 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.

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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?

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• What if Kathleens 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 Kathleens claim-or
  Hypothesis.

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Steps in Hypothesis Testing 1. A claim is made.
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.
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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.
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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 p43 H1 p 43
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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.

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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.

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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.
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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.
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What if our sample resulted in a sample mean of
2.95 minutes?
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Hypothesis testing is a procedure, based on
sample evidence and probability, used to test
claims regarding a characteristic of one or more
populations.
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The null hypothesis, denoted Ho (read
H-naught), 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.
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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
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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 lt some value
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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 lt some value 3. Equal
versus greater than (right-tailed test) Ho
parameter some value H1 parameter gt some value
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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.

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Four Outcomes from Hypothesis Testing 1. We could
reject Ho when in fact H1 is true. This would be
a correct decision.
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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.
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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.
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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.
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• 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.

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CAUTION!
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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.