Chapter 8
Hypothesis Testing
Section 8-2
Steps in Hypothesis Testing –
Traditional Method
Example 1
Section 8-2 Exercise #12b
Using the z table find the critical value (or values).
 = 0.01
Left tail
Section 8-2 Exercise #12g
Using the z table find the critical value (or values).
 = 0.05
Right tail
Section 8-2 Exercise #12h
Using the z table find the critical value (or values).
 = 0.01
Two - tailed test.
Chapter 8
Hypothesis Testing
Section 8-3
z Test for a Mean
Example 2
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?
Chapter 8
Hypothesis Testing
Section 8-3
Exercise #7
25
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25
30
26.5
26
25.5
29.5
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31.5
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29.5
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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?
Chapter 8
Hypothesis Testing
Section 8-3
Exercise #13
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.
Chapter 8
Hypothesis Testing
Section 8-3
Exercise #17
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 company’s
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.
Chapter 8
Hypothesis Testing
Section 8-4
t Test for a Mean
Chapter 8
Hypothesis Testing
Section 8-4
Exercise #3a
Find the critical value (or values) for the t test for each.
n = 10
 = 0.05
Right - tailed
d.f . = 9
C.V. = + 1.833
Chapter 8
Hypothesis Testing
Section 8-4
Exercise #3b
Find the critical value (or values) for the t test for each.
n = 18
 = 0.10
Two - tailed
Chapter 8
Hypothesis Testing
Section 8-4
Exercise #3c
Find the critical value (or values) for the t test for each.
n=6
 = 0.01
Left - tailed
Chapter 8
Hypothesis Testing
Section 8-4
Exercise #7
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?
Chapter 8
Hypothesis Testing
Section 8-4
Exercise #9
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:
485 511 841 725 615
520 535 635 616 582
At  = 0.025, is there enough
evidence to reject the claim?
Example 3
Chapter 8
Hypothesis Testing
Section 8-4
Exercise #13
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?
Chapter 8
Hypothesis Testing
Section 8-4
Exercise #17
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.
H0 :  = 5.8 (claim) H1 :   5.8
Chapter 8
Hypothesis Testing
Section 8-5
z Test for a Proportion
Chapter 8
Hypothesis Testing
Section 8-5
Exercise #7
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%?
H0 : p = 0.40
H1 : p  0.40 (claim)
Chapter 8
Hypothesis Testing
Section 8-5
Exercise #9
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 .
H0 : p = 0.63 (claim)
H1 : p  0.63
Chapter 8
Hypothesis Testing
Section 8-5
Exercise #15
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.
Chapter 8
Hypothesis Testing
Section 8-5
Exercise #19
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 ?
H0 : p  0.576
H1: p < 0.576 (claim)
Chapter 8
Hypothesis Testing
Section 8-6
c2 Test for a Variance or
Standard Deviation
Chapter 8
Hypothesis Testing
Section 8-6
Exercise #5
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.
H1 :  < 15 (claim)
H0 :   15
Chapter 8
Hypothesis Testing
Section 8-6
Exercise #7
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.
H0 :  1.2 (claim)
H1 :  > 1.2
Chapter 8
Hypothesis Testing
Section 8-6
Exercise #9
290 320 260 220 300 310 310 270 250 230
270 260 310 200 250 250 270 210 260 300
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?
Chapter 8
Hypothesis Testing
Section 8-6
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?