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C H A P T E R E I G H T
Hypothesis Testing
1.1
Descriptive and Inferential Statistics
Slide 2
Copyright © 2012 The McGraw-Hill Companies, Inc. 8-1Steps
in Hypothesis Testing—Traditional Method8-2z Test for a
Mean8-3t Test for a Mean8-4z Test for a Proportion8-
for a Variance or Standard Deviation8-6Additional Topics
Regarding Hypothesis
Testing
Hypothesis Testing
CHAPTER
8
Outline

1.1
Descriptive and inferential statistics
1Understand the definitions used in hypothesis
testing.2State the null and alternative hypotheses.3Find critical
values for the z test.4State the five steps used in hypothesis
using the z test.
Learning Objectives
1.1
Descriptive and inferential statistics
8Test variances or standard deviations, using the chi-square
test.9Test hypotheses, using confidence intervals.10Explain the
relationship between type I and type II errors and the power of a

test.
Learning Objectives
Hypothesis Testing
Three methods used to test hypotheses:
1. The traditional method
2. The P-value method
3. The confidence interval method
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8.1 Steps in Hypothesis Testing-Traditional Method
A statistical hypothesis is a conjecture about a population
parameter. This conjecture may or may not be true.
The null hypothesis, symbolized by H0, is a statistical
hypothesis that states that there is no difference between a
parameter and a specific value, or that there is no difference
between two parameters.
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Steps in Hypothesis Testing-Traditional Method
The alternative hypothesis, symbolized by H1, is a statistical

hypothesis that states the existence of a difference between a
parameter and a specific value, or states that there is a
difference between two parameters.
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Situation A
A medical researcher is interested in finding out whether a new
medication will have any undesirable side effects. The
researcher is particularly concerned with the pulse rate of the
patients who take the medication. Will the pulse rate increase,
decrease, or remain unchanged after a patient takes the
medication? The researcher knows that the mean pulse rate for
the population under study is 82 beats per minute.
The hypotheses for this situation are
This is called a two-tailed hypothesis test.
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Situation B
A chemist invents an additive to increase the life of an
automobile battery. The mean lifetime of the automobile

battery without the additive is 36 months.
In this book, the null hypothesis is always stated using the
equals sign. The hypotheses for this situation are
This is called a right-tailed hypothesis test.
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Situation C
A contractor wishes to lower heating bills by using a special
type of insulation in houses. If the average of the monthly
heating bills is $78, her hypotheses about heating costs with the
use of insulation are
This is called a left-tailed hypothesis test.
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Claim
When a researcher conducts a study, he or she is generally
looking for evidence to support a claim. Therefore, the claim
should be stated as the alternative hypothesis, or research
hypothesis.
A claim, though, can be stated as either the null hypothesis or
the alternative hypothesis; however, the statistical evidence can
only support the claim if it is the alternative hypothesis.
Statistical evidence can be used to reject the claim if the claim
is the null hypothesis.
These facts are important when you are stating the conclusion
of a statistical study.
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Hypothesis Testing
After stating the hypotheses, the researcher’s next step is to
design the study. The researcher selects the correct statistical
test, chooses an appropriate level of significance, and
formulates a plan for conducting the study.
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Hypothesis Testing
A statistical test uses the data obtained from a sample to make a
decision about whether the null hypothesis should be rejected.
The numerical value obtained from a statistical test is called the
test value.
In the hypothesis-testing situation, there are four possible
outcomes.
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Hypothesis Testing
In reality, the null hypothesis may or may not be true, and a
decision is made to reject or not to reject it on the basis of the
data obtained from a sample.
A type I error occurs if one rejects the null hypothesis when it
is true.
A type II error occurs if one does not reject the null hypothesis
when it is false.
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Hypothesis Testing
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Hypothesis Testing
The level of significance is the maximum probability of
committing a type I error. This probability is symbolized by a
(alpha). That is,
P(type I error) = a.
Likewise,
P(type II error) = b (beta).
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Hypothesis Testing
Typical significance levels are:
0.10, 0.05, and 0.01
For example, when a = 0.10, there is a 10% chance of rejecting
a true null hypothesis.
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Hypothesis Testing
The critical or rejection region is the range of values of the test
value that indicates that there is a significant difference and that
the null hypothesis should be rejected.

The noncritical or nonrejection region is the range of values of
the test value that indicates that the difference was probably due
to chance and that the null hypothesis should not be rejected.
The critical value, C.V., separates the critical region from the
noncritical region.
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Hypothesis Testing
Finding the Critical Value for α = 0.01 (Right-Tailed Test)
z = 2.33 for α = 0.01 (Right-Tailed Test)
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Hypothesis Testing
Finding the Critical Value for α = 0.01 (Left-Tailed Test)
Because of symmetry,
z = –2.33 for α = 0.01 (Left-Tailed Test)
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Hypothesis Testing
Finding the Critical Value for α = 0.01 (Two-Tailed Test)
z = ±2.58
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8.1
Steps in Hypothesis Testing—Traditional Method
Finding the Critical Values for Specific α Values, Using Table
E
Step 1 Draw the figure and indicate the appropriate area.
If the test is left-tailed, the critical region, with an area equal
to α, will be on the left side of the mean.
If the test is right-tailed, the critical region, with an area equal
to α, will be on the right side of the mean.

If the test is two-tailed, α must be divided by 2; one-half of the
area will be to the right of the mean, and one-half will be to the
left of the mean.
Procedure Table
8.1
Finding the Critical Values for Specific α Values, Using Table
E
Step 2
For a left-tailed test, use the z value that corresponds to the area
equivalent to α in Table E.
For a right-tailed test, use the z value that corresponds to the
area equivalent to 1 – α.
For a two-tailed test, use the z value that corresponds to α/2 for
the left value. It will be negative. For the right value, use the z
value that corresponds to the area equivalent to 1 – α/2. It will
be positive.
Procedure Table

Chapter 8
Hypothesis Testing
Section 8-1
Example 8-2
Page #423
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Using Table E in Appendix C, find the critical value(s) for each
situation and draw the appropriate figure, showing the critical
region.
a. A left-tailed test with α = 0.10.
Step 2 Find the area closest to 0.1000 in Table E. In this case,
it is 0.1003. The z value is –1.28.
Example 8-2: Using Table E
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region.
b. A two-tailed test with α = 0.02.
Step 1 Draw the figure with areas α /2 = 0.02/2 = 0.01.
Step 2 Find the areas closest to 0.01 and 0.99.
The areas are 0.0099 and 0.9901.
The z values are –2.33 and 2.33.
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region.

c. A right-tailed test with α = 0.005.
Step 2 Find the area closest to 1 – α = 0.995.
There is a tie: 0.9949 and 0.9951. Average the z values of 2.57
and 2.58 to get 2.575 or 2.58.
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8.1
Solving Hypothesis-Testing Problems
(Traditional Method)

Step 1 State the hypotheses and identify the claim.
Step 2 Find the critical value(s) from the appropriate table in
Appendix C.
Step 3 Compute the test value.
Step 4 Make the decision to reject or not reject the null
hypothesis.
Step 5 Summarize the results.
Procedure Table
8.2 z Test for a Mean
The z test is a statistical test for the mean of a population. It
distributed
The formula for the z test is
where
= sample mean
μ = hypothesized population mean
n = sample size
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Chapter 8
Hypothesis Testing
Section 8-2
Example 8-3
Page #427
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Example 8-3: Intelligence Tests
In Pennsylvania the average IQ score is 101.5. The variable is
normally distributed, and the population standard deviation is
15. A school superintendent claims that the students in her
school district have an IQ higher than the average of 101.5. She
selects a random sample of 30 students and finds the mean of
the test scores is 106.4. Test the claim at a 0.05.
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Step 2 Find the critical value. Since α = 0.05 and the test is a
right-tailed test, the critical value is
z = +1.65.
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Step 4 Make the decision. Since the test value, 1.79, is
greater than the critical value, 1.65, the decision is to reject the
null hypothesis.
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Example 8-3: Days on Dealers’ Lots
There is enough evidence to support the claim
that the IQ of the students is higher than the state
average IQ.
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Important Comments
In Example 8–3, the difference is said to be statistically
significant. However, when the null hypothesis is rejected, there
is always a chance of a type I error. In this case, the probability
of a type I error is at most 0.05, or 5%.
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Chapter 8
Hypothesis Testing
Section 8-2

Example 8-4
Page #429
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Example 8-4: SAT Tests
For a specific year, the average score on the SAT Math test was
515.* The variable is normally distributed, and the population
standard deviation is 100. The same superintendent in the
previous example wishes to see if her students scored
significantly below the national average on the test. She
randomly selected 36 student scores, as shown. At a 0.10, is
there enough evidence to support the claim?
496 506 507 505 438 499
505 522 531 762 513 493
522 668 543 519 349 506
519 516 714 517 511 551
287 523 576 516 515 500
243 509 523 503 414 504
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Step 1: Find the critical value.
State the hypotheses and identify the claim.
Since α = 0.10 and the test is a left-tailed test, the critical value
is z = –1.28.
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Step 3: Compute the test value.
Since the exercise gives raw data find the mean of the data.
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Step 4: Make the decision.
Since the test value, –1.36, falls in the noncritical region, the
decision is to not reject the null hypothesis.
Step 5: Summarize the results.
There is not enough evidence to support the
claim that the students scored below the national
average.
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Chapter 8
Hypothesis Testing
Section 8-2
Example 8-5
Page #430
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Example 8-5: Cost of Rehabilitation
The Medical Rehabilitation Education Foundation reports that
the average cost of rehabilitation for stroke victims is $24,672.
To see if the average cost of rehabilitation is different at a
particular hospital, a researcher selects a random sample of 35
stroke victims at the hospital and finds that the average cost of
their rehabilitation is $26,343. The standard deviation of the
population is $3251. At α = 0.01, can it be concluded that the
average cost of stroke rehabilitation at a particular hospital is
different from $24,672?
Step 1: State the hypotheses and identify the claim.
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The Medical Rehabilitation Education Foundation reports that
the average cost of rehabilitation for stroke victims is $24,672.
To see if the average cost of rehabilitation is different at a
particular hospital, a researcher selects a random sample of 35
stroke victims at the hospital and finds that the average cost of
their rehabilitation is $26,343. The standard deviation of the
population is $3251. At α = 0.01, can it be concluded that the

average cost of stroke rehabilitation at a particular hospital is
different from $24,672?
Since α = 0.01 and a two-tailed test, the critical values are z =
±2.58.
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Step 3: Find the test value.
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Reject the null hypothesis, since the test value falls in the
critical region.

There is enough evidence to support the claim that the average
cost of rehabilitation at the particular hospital is different from
$24,672.
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Hypothesis Testing
The P-value (or probability value) is the probability of getting a
sample statistic (such as the mean) or a more extreme sample
statistic in the direction of the alternative hypothesis when the
null hypothesis is true.
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Hypothesis Testing
Decision rule when using a P-value
If P-value reject the null hypothesis

If P-value do not reject the null hypothesis
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8.2
z Test for a Mean
Solving Hypothesis-Testing Problems (P-Value Method)
Step 3 Find the P-value.
Step 4 Make the decision.
Procedure Table

Chapter 8
Hypothesis Testing
Section 8-2
Example 8-6
Page #432
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Example 8-6: Cost of College Tuition
A researcher wishes to test the claim that the average cost of
tuition and fees at a four-year public college is greater than
$5700. She selects a random sample of 36 four-year public
colleges and finds the mean to be $5950. The population
standard deviation is $659. Is there evidence to support the
claim at a 0.05? Use the P-value method.
H0: μ = $5700 and H1: μ > $5700 (claim)
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Step 3: Find the P-value.
Using Table E, find the area for z = 2.28.
The area is 0.9887.
Subtract from 1.0000 to find the area of the tail.
Hence, the P-value is 1.0000 – 0.9887 = 0.0113.
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Since the P-value is less than 0.05, the decision is to reject the
null hypothesis.
There is enough evidence to support the claim that the tuition
and fees at four-year public colleges are greater than $5700.
Note: If α = 0.01, the null hypothesis would not be rejected.
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Chapter 8
Hypothesis Testing
Section 8-2

Example 8-7
Page #432
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Example 8-7: Wind Speed
A researcher claims that the average wind speed in a certain city
is 8 miles per hour. A sample of 32 days has an average wind
speed of 8.2 miles per hour. The standard deviation of the
population is 0.6 mile per hour. At α = 0.05, is there enough
evidence to reject the claim? Use the P-value method.
H0: μ = 8 (claim) and H1: μ ≠ 8
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A researcher claims that the average wind speed in a certain city
is 8 miles per hour. A sample of 32 days has an average wind
speed of 8.2 miles per hour. The standard deviation of the
population is 0.6 mile per hour. At α = 0.05, is there enough
evidence to reject the claim? Use the P-value method.
The area for z = 1.89 is 0.9706.
Subtract: 1.0000 – 0.9706 = 0.0294.
Since this is a two-tailed test, the area of 0.0294 must be
doubled to get the P-value.
The P-value is 2(0.0294) = 0.0588.
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The decision is to not reject the null hypothesis, since the P-
value is greater than 0.05.
There is not enough evidence to reject the claim that the
average wind speed is 8 miles per hour.

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Guidelines for P-Values With No α
If P-
highly significant.
If P-value > 0.01 but P- othesis.
The difference is significant.
If P-value > 0.05 but P-
of type I error before rejecting the null hypothesis.
If P-value > 0.10, do not reject the null hypothesis. The
difference is not significant.
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Significance
The researcher should distinguish between statistical
significance and practical significance.
When the null hypothesis is rejected at a specific significance
level, it can be concluded that the difference is probably not due

to chance and thus is statistically significant. However, the
results may not have any practical significance.
It is up to the researcher to use common sense when interpreting
the results of a statistical test.
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8.3 t Test for a Mean
The t test is a statistical test for the mean of a population and is
used when the population is normally or approximately
The formula for the t test is
The degrees of freedom are d.f. = n – 1.
Note: When the degrees of freedom are above 30, some
textbooks will tell you to use the nearest table value; however,
in this textbook, you should round down to the nearest table
value. This is a conservative approach.
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Chapter 8
Hypothesis Testing
Section 8-3
Example 8-8
Page #442
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Example 8-8: Table F
Find the critical t value for α = 0.05 with d.f. = 16 for a right-
tailed t test.
Find the 0.05 column in the top row and 16 in the left-hand
column.
The critical t value is +1.746.
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Chapter 8
Hypothesis Testing

Section 8-3
Examples 8-9 & 8-10
Page #443
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Find the critical t value for α = 0.01 with d.f. = 22 for a left-
tailed test.
Find the 0.01 column in the One tail row, and 22 in the d.f.
column.
The critical value is t = –2.508 since the test is a one-tailed left
test.
Find the critical value for α = 0.10 with d.f. = 18 for a two-
tailed t test.
Find the 0.10 column in the Two tails row, and 18 in the d.f.
column.
The critical values are 1.734 and –1.734.
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Chapter 8
Hypothesis Testing
Section 8-3
Example 8-12
Page #444
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Example 8-12: Hospital Infections
A medical investigation claims that the average number of
infections per week at a hospital in southwestern Pennsylvania
is 16.3. A random sample of 10 weeks had a mean number of
17.7 infections. The sample standard deviation is 1.8. Is there
enough evidence to reject the investigator’s claim at α = 0.05?
The critical values are 2.262 and –2.262 for α = 0.05 and
d.f. = 9.

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A medical investigation claims that the average number of
infections per week at a hospital in southwestern Pennsylvania
is 16.3. A random sample of 10 weeks had a mean number of
17.7 infections. The sample standard deviation is 1.8. Is there
enough evidence to reject the investigator’s claim at α = 0.05?
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Reject the null hypothesis since 2.46 > 2.262.

There is enough evidence to reject the claim that the average
number of infections is 16.3.
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Chapter 8
Hypothesis Testing
Section 8-3
Example 8-13
Page #444
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Example 8-13: Starting Nurse Salary
According to payscale.com, the average starting salary for a
nurse practitioner is $79,500. A researcher wishes to test the

claim that the starting salary is less than $79,500. A random
sample of 8 starting nurse practitioners is selected, and their
starting salaries (in dollars) are shown. Is there enough
evidence to support the researcher’s claim at a 0.10? Assume
the variable is normally distributed.
82,000 68,000 70,200 75,600
83,500 64,300 78,600 79,000
At α = 0.10 and d.f. = 7, the critical value is –1.415.
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Compute the test value. In this case, the mean and
standard deviation must be found. Use the formulas in
Chapter 3 or your calculator.
X = $75,150 and s = $6,937.68
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Do not reject the null hypothesis since –0.773 falls in the
critical region.
There is enough evidence to support the claim that
the average starting salary for nurse practitioners is less
than $79,500.
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Chapter 8
Hypothesis Testing
Section 8-3
Example 8-16
Page #447
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Example 8-16: Jogger’s Oxygen Uptake
A physician claims that joggers’ maximal volume oxygen
uptake is greater than the average of all adults. A sample of 15
joggers has a mean of 40.6 milliliters per kilogram (ml/kg) and
a standard deviation of 6 ml/kg. If the average of all adults is
36.7 ml/kg, is there enough evidence to support the physician’s
claim at α = 0.05?
H0: μ = 36.7 and H1: μ > 36.7 (claim)
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A physician claims that joggers’ maximal volume oxygen
uptake is greater than the average of all adults. A sample of 15

joggers has a mean of 40.6 milliliters per kilogram (ml/kg) and
a standard deviation of 6 ml/kg. If the average of all adults is
36.7 ml/kg, is there enough evidence to support the physician’s
claim at α = 0.05?
In the d.f. = 14 row, 2.517 falls between 2.145 and 2.624,
corresponding to α = 0.025 and α = 0.01.
Thus, the P-value is somewhere between 0.01 and 0.025, since
this is a one-tailed test.
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The decision is to reject the null hypothesis, since the P-value <
0.05.
There is enough evidence to support the claim that the joggers’
maximal volume oxygen uptake is greater than 36.7 ml/kg.
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Whether to use z or t
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8.4 z Test for a Proportion
Since a normal distribution can be used to approximate the
normal distribution can be used to test hypotheses for
proportions.
The formula for the z test for a proportion is
where
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Chapter 8

Hypothesis Testing
Section 8-4
Example 8-17
Page #454
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Example 8-17: Obese Young People
A researcher claims that based on the information obtained from
the Centers for Disease Control and Prevention, 17% of young
people ages 2–19 are obese. To test this claim, she randomly
selected 200 people ages 2–19 and found that 42 were obese. At
a = 0.05, is there enough evidence to reject the claim?
Since α = 0.05 and the test is a two-tailed test, the critical
values are ±1.96.
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A researcher claims that based on the information obtained from
the Centers for Disease Control and Prevention, 17% of young
people ages 2–19 are obese. To test this claim, she randomly
selected 200 people ages 2–19 and found that 42 were obese. At
a = 0.05, is there enough evidence to reject the claim?
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Do not reject the null hypothesis since the test value falls in the
noncritical region.
There is not enough evidence to reject the claim that
17% of young people ages 2–19 are obese.
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Chapter 8
Hypothesis Testing
Section 8-4
Example 8-18
Page #454
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Example 8-18: Female Gun Owners
The Gallup Crime Survey stated that 23% of gun owners are
women. A researcher believes that in the area where he lives,
the percentage is less than 23%. He randomly selects a sample
of 100 gun owners and finds that 11% of the gun owners are
women. At a = 0.01, is the percentage of female gun owners in
his area less than 23%.
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Step 2 Find the critical value(s). Since α = 0.01 and this test
is one-tailed, the critical value is -2.33.
Step 3 Compute the test value. In this case, is given
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Step 4 Make the decision. Reject the null
hypothesis since the test value falls in the critical
region.
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There is enough evidence to support the claim
that the percentage of female gun owners in that
area is less than 23%.
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Characteristics of the Chi-square Distribution
All chi-square values are
The chi-square distribution is a family of curves based on the
degrees of freedom.
The area under each chi-square distribution is equal to 1.
The chi-square distributions are positively skewed.
Bluman, Chapter 8
88

Characteristics of the Chi-square Distribution
to find the area use table G in appendix A.
Finding the chi-square critical value for a specific a when the
hypothesis test is right-tailed
Finding the chi-square critical value for a specific a when the
hypothesis test is left-tailed
Finding the chi-square critical values for a specific a when the
hypothesis test is two-tailed
Bluman, Chapter 8
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Chapter 8
Hypothesis Testing
Section 8-5
Example 8-21
Page #461
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Example 8-21: Table G
Find the critical chi-square value for 15 degrees of freedom
when α = 0.05 and the test is right-tailed.

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Chapter 8
Hypothesis Testing
Section 8-5
Example 8-22
Page #462
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when α = 0.05 and the test is left-tailed.
When the test is left-tailed, the α value must be subtracted from
1, that is, 1 – 0.05 = 0.95. The left side of the table is used,
because the chi-square table gives the area to the right of the

critical value, and the chi-square statistic cannot be negative.
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when α = 0.05 and the test is left-tailed.
Use Table G, looking in row 10 and column 0.95.
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8.5 Test for a Variance or a Standard Deviation
The chi-square distribution is also used to test a claim about a
single variance or standard deviation.
The formula for the chi-square test for a variance is

with degrees of freedom d.f. = n – 1 and
n = sample size
s2 = sample variance
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Assumptions for the Test for a Variance or a Standard
Deviation
The sample must be randomly selected from the population.
The population must be normally distributed for the variable
under study.
The observations must be independent of one another.
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Chapter 8
Hypothesis Testing
Section 8-5
Example 8-23
Page #462
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when α = 0.05 and a two-tailed test is conducted.
When the test is two-tailed, the area must be split. The area to
the right of the larger value is α /2, or 0.025. The area to the
right of the smaller value is 1 – α /2, or 0.975.
With 22 degrees of freedom, areas 0.025 and 0.975 correspond
to chi-square values of 36.781 and 10.982.
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Chapter 8
Hypothesis Testing
Section 8-5
Example 8-24
Page #464
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Example 8-24: Math SAT Test
The standard deviation for the Math SAT test is 100. The
variance is 10,000. An instructor wishes to see if the variance of
the 23 randomly selected students in her school is less than
10,000. The variance for the 23 test scores is 7225. Is there
enough evidence to support the claim that the variance of the
students in her school is less than 10,000 at a = 0.05? Assume
that the scores are normally distributed.
The critical value is 12.338.
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An instructor wishes to see whether the variation in scores of
the 23 students in her class is less than the variance of the
population. The variance of the class is 198. Is there enough
evidence to support the claim that the variation of the students

Assume that the scores are normally distributed.
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Do not reject the null hypothesis since the test value 15.895
falls in the noncritical region.
There is not enough evidence to support the claim that the
variation of the students’ test scores is less than the
population variance.
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Chapter 8
Hypothesis Testing
Section 8-5
Example 8-26
Page #450
103
Bluman Chapter 8
103
Example 8-26: Nicotine Content
A cigarette manufacturer wishes to test the claim that the
variance of the nicotine content of its cigarettes is 0.644.
Nicotine content is measured in milligrams, and assume that it
is normally distributed. A sample of 20 cigarettes has a standard
deviation of 1.00 milligram. At α = 0.05, is there enough
evidence to reject the manufacturer’s claim?
The critical values are 32.852 and 8.907.
104
Bluman Chapter 8

104
A cigarette manufacturer wishes to test the claim that the
variance of the nicotine content of its cigarettes is 0.644.
Nicotine content is measured in milligrams, and assume that it
is normally distributed. A sample of 20 cigarettes has a standard
deviation of 1.00 milligram. At α = 0.05, is there enough
evidence to reject the manufacturer’s claim?
The standard deviation s must be squared in the formula.
105
Bluman Chapter 8
105
Do not reject the null hypothesis, since the test value falls in
the noncritical region.

There is not enough evidence to reject the manufacturer’s claim
that the variance of the nicotine content of the cigarettes is
0.644.
106
Bluman Chapter 8
106
8.6 Additional Topics Regarding Hypothesis Testing
There is a relationship between confidence intervals and
hypothesis testing.
When the null hypothesis is rejected in a hypothesis-testing
situation, the confidence interval for the mean using the same
level of significance will not contain the hypothesized mean.
Likewise, when the null hypothesis is not rejected, the
confidence interval computed using the same level of
significance will contain the hypothesized mean.
107
Bluman Chapter 8

Chapter 8
Hypothesis Testing
Section 8-6
Example 8-30
Page #474
108
Bluman Chapter 8
108
Example 8-30: Sugar Production
Sugar is packed in 5-pound bags. An inspector suspects the bags
may not contain 5 pounds. A sample of 50 bags produces a
mean of 4.6 pounds and a standard deviation of 0.7 pound. Is
there enough evidence to conclude that the bags do not contain
5 pounds as stated at α = 0.05? Also, find the 95% confidence
interval of the true mean.
Step 2: Find the critical values.
The critical values are t = ±2.010.
109
Bluman Chapter 8

109
Sugar is packed in 5-pound bags. An inspector suspects the bags
may not contain 5 pounds. A sample of 50 bags produces a
mean of 4.6 pounds and a standard deviation of 0.7 pound. Is
there enough evidence to conclude that the bags do not contain
5 pounds as stated at α = 0.05? Also, find the 95% confidence
interval of the true mean.
110
Bluman Chapter 8
110
Since -4.04 -2.014, the null hypothesis is rejected.
There is enough evidence to support the claim that the bags do
not weigh 5 pounds.

111
Bluman Chapter 8
111
The 95% confidence interval for the mean is
Notice that the 95% confidence interval of m does not contain
the hypothesized value μ = 5.
Hence, there is agreement between the hypothesis test and the
confidence interval.
112
Bluman Chapter 8
112
The power of a test measures the sensitivity of the test to detect
a real difference in parameters if one actually exists. The
higher the power, the more sensitive the test. The power is 1 –
β.
Power of a Statistical Test

113
Bluman Chapter 8
113
1
:82
H
m
¹
0
:82
H
m
=
1
:36
H
m
>
0
:36
H
m
=
1
:78
H
m
<
0

:78
H
m
=
-
=
X
z
n
m
s
X
26,34324,672
325135
-
=
3.04
=
59505700
65936
-
=
2.28
=
8.28
0.632
-
=
1.89
=
-
=
X
t
sn
m

-
=
X
z
sn
m
17.716.3
1.810
-
=
2.46
=
-
=
X
t
sn
m
40.636.7
615
-
=
2.517
=
ˆ
-
=
pp
z
pqn
(
)
ˆ
sample proportion
population proportion
sample size

X
p
n
p
n
=
=
=
ˆ
p
2
24.996
=
c
2
3.940
=
c
(
)
2
2
2
1
-
=
ns
c
s
2
c
(
)
2
2
2

1
-
=
ns
c
s
(
)
(
)
2
191.00
0.644
=
29.5
=
X
t
sn
m
-
=
4.65.0
0.750
-
=
4.04
=-

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