Steps in Hypothesis Testing

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Section 8-2
Chapter 8 Hypothesis Testing
Steps in Hypothesis Testing Traditional Method
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Example 1
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Section 8-2 Exercise 12b
Using the z table find the critical value (or
values).
Left tail
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Section 8-2 Exercise 12g
Using the z table find the critical value (or
values).
Right tail
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Section 8-2 Exercise 12h
Using the z table find the critical value (or
values).
Two - tailed test.
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Section 8-3
Chapter 8 Hypothesis Testing
z Test for a Mean
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Example 2
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Section 8-3 Exercise 5
A report in USA TODAY stated that the average age
of commercial jets in the United States is 14
years. An executive of a large airline company
selects a sample of 36 planes and finds the
average age of the planes is 11.8 years. The
standard deviation of the sample is 2.7 years.
At ? 0.01, can it be concluded that the
average age of the planes in his Company is
less than the national average?
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Section 8-3
Chapter 8 Hypothesis Testing
Exercise 7
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25 32 35 25 30 26.5 26 25.5 29.5 32
30 28.5 30 32 28 31.5 29 29.5 30 34
29 32 27 28 33 28 27 32 29 29.5
The average one-year-old (both sexes) is 29
inches tall. A random sample of 30 one-year-olds
in a large day care franchise resulted in the
following heights. At ? 0.05, can it be
concluded that the average height differs from
29 inches?
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Section 8-3
Chapter 8 Hypothesis Testing
Exercise 13
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To see if young men ages 8 through 17 years spend
more or less than the national average of 24.44
per shopping trip to a local mall, the
manager surveyed 33 young men and found the
average amount spent per visit was 22.97. The
standard deviation of the sample was 3.70. At
? 0.02, can it be concluded that the average
amount spent at a local mall is not equal to the
national average of 24.44.
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Section 8-3
Chapter 8 Hypothesis Testing
Exercise 17
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A study found that the average stopping distance
of a school bus traveling 50 miles per hour was
264 feet (Snapshot, USA TODAY, March12, 1992). A
group of automotive engineers decided to conduct
a study of its school buses and found that for 20
buses, the average stopping distance of buses
traveling 50 miles per hour was 262.3 feet. The
standard deviation of the population was 3 feet.
Test the claim that the average stopping
distance of the companys buses is actually less
than 264 feet. Find the P-value. On the basis of
the P-value, should the null hypothesis be
rejected at ? 0.01? Assume that the variable
isnormally distributed.
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Section 8-4
Chapter 8 Hypothesis Testing
t Test for a Mean
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Section 8-4
Chapter 8 Hypothesis Testing
Exercise 3a
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Find the critical value (or values) for the t
test for each.
Right - tailed
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Section 8-4
Chapter 8 Hypothesis Testing
Exercise 3b
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Find the critical value (or values) for the t
test for each.
Two - tailed
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Section 8-4
Chapter 8 Hypothesis Testing
Exercise 3c
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Find the critical value (or values) for the t
test for each.
Left - tailed
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Section 8-4
Chapter 8 Hypothesis Testing
Exercise 7
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• The average salary of graduates entering the
  actuarial
• field is reported to be 40,000. To test this,
• a statistics professor surveys 20 graduates
• and finds their average salary to be 43,228
• with a standard deviation of 4,000. Using
• ? 0.05, has he shown the reported
• salary incorrect?

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Section 8-4
Chapter 8 Hypothesis Testing
Exercise 9
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A researcher estimates that the average height of
the buildings of 30 or more stories in a large
city is at least 700 feet. A random sample of 10
buildings is selected, and the heights in feet
are shown 485 511 841 725 615520 535 635 616 5
82 At ? 0.025, is there enough evidence to
reject the claim?
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Example 3
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Section 8-4
Chapter 8 Hypothesis Testing
Exercise 13
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Last year the average cost of making a movie was
54.8 million. This year, a random sample of 15
recent action movies had an average production
cost of 62.3 million with a variance of 90.25
million.At the 0.05 level of significance, can
it be concluded that it costs more than average
to produce an action movie?
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Section 8-4
Chapter 8 Hypothesis Testing
Exercise 17
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A report by the Gallup Poll stated that on
average a woman visits her physician 5.8
times a year. A researcher randomly
selected 20 women and the following data
was obtained.
3 2 1 3 7 2 9 4 6 6
8 0 5 6 4 2 1 3 4 1
At ? 0.05 can it be concluded that the average
is still 5.8? Use the P - value method.
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Section 8-5
Chapter 8 Hypothesis Testing
z Test for a Proportion
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Section 8-5
Chapter 8 Hypothesis Testing
Exercise 7
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It has been reported that 40 of the adult
population participates in computer hobbies
during their leisure time. A random sample of 180
adults found that 65 engaged in computer
hobbies. At ? 0.01, is there sufficient
evidence to conclude that the proportion
differs from 40?
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Section 8-5
Chapter 8 Hypothesis Testing
Exercise 9
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• An item in USA TODAY reported that 63 of
  Americans owned an answering machine. A survey of
  143 employees at a large school showed that
• 85 owned an answering machine. At
• 0.05, test the claim that the
• percentage is the same as
• stated in USA TODAY .

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Section 8-5
Chapter 8 Hypothesis Testing
Exercise 15
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Researchers suspect that 18 of all high school
students smoke at least one pack of cigarettes a
day. At Wilson High School, with an enrollment of
300 students, a study found that 50
students smoked at least one pack of cigarettes
a day. At ? 0.05, test the claim that 18 of
all high school students smoke at least one pack
of cigarettes a day. Use the P - value method.
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Section 8-5
Chapter 8 Hypothesis Testing
Exercise 19
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A report by the NCAA states that 57.6 of
football injuries occur during practices. A head
trainer claims that this is too high for his
conference, so he randomly selects 36 injuries
and finds that 17 occurred during practices. Is
his claim correct, using ? 0.05 ?
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Section 8-6
Chapter 8 Hypothesis Testing
c2 Test for a Variance or Standard Deviation
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Section 8-6
Chapter 8 Hypothesis Testing
Exercise 5
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Test the claim that the standard deviation of the
number of aircraft stolen each year in the
United States is less than 15 if a sample of 12
years had a standard deviation of 13.6. Use ?
0.05.
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Section 8-6
Chapter 8 Hypothesis Testing
Exercise 7
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The manager of a large company claims that the
standard deviation of the time (in minutes) that
it takes a telephone call to be transferred to
the correct office in her company is 1.2 minutes
or less. A sample of 15 calls is selected, and
the calls are timed. The standard deviation of
the sample is 1.8 minutes. At ? 0.01, test
the claim that the standard deviation is less
than or equal to 1.2 minutes. Use the P-value
method.
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Section 8-6
Chapter 8 Hypothesis Testing
Exercise 9
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300
A random sample of 20 different kinds of
doughnuts had the following calorie contents. At
? 0.01, is there sufficient evidence to
conclude that the standard deviation is greater
than 20 calories?
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Section 8-6
Chapter 8 Hypothesis Testing
Exercise 13
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A random sample of home run totals for National
League Home Run Champions from 1938 to 2001 is
shown. At the 0.05 level of significance, is
there sufficient evidence to conclude that the
variance is greater than 25?
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