Business Statistics: A First Course

1
Business Statistics A First Course

• Fundamentals of Hypothesis TestingChapter 9
  Examples

2
Identifying Hypotheses Thinking Challenge
What Are the Hypotheses?

• 1. Is the population average amount of TV viewing
  12 hours?
• 2. Is the population average amount of TV viewing
  different from 12 hours?
• 3. Is the average cost per hat less than or equal
  to 20?
• 4. Is the average amount spent in the bookstore
  greater than 25?

3
Identifying Hypotheses Solution

• 1. Is the population average amount of TV viewing
  12 hours?
• ?X 12 ?X ? 12 H0 ?X 12 H1 ?X ? 12
• 2. Is the population average amount of TV viewing
  different from 12 hours?
• ?X ? 12 ?X 12 H0 ?X 12 H1 ?X ? 12

4
Identifying Hypotheses Solution

• 3. Is the average cost per hat less than or equal
  to 20?
• ?X ? 20 ?X ? 20 H0 ?X ? 20 H1 ?X ? 20
• 4. Is the average amount spent in the bookstore
  greater than 25?
• ?X ? 25 ?X ? 25 H0 ?X ? 25 H1 ?X ? 25

5
Two-Tailed Z Test Thinking Challenge

• Youre a Q/C inspector. You want to find out if
  a new machine is making electrical cords to
  customer specification average breaking strength
  of 70 lb. with ?X 3.5 lb. You take a sample of
  36 cords compute a sample mean of 69.7 lb. At
  the .05 level, is there evidence that the machine
  is not meeting the average breaking strength?

6
Solution Template

• H0
• H1
• ?
• n
• Critical Value(s)

Test Statistic Decision Conclusion
0
Z
7
Two-Tailed Z Test Solution

• H0 ?X 70
• H1 ?X ? 70
• ? .05
• n 36
• Critical Value(s)

Test Statistic Decision Conclusion
X
?
?
?
69
7
70
.
x
Z
?
?
?
?
51
.
?
3
5
.
x
n
36
Reject H
Reject H
Do Not Reject at ? .05
0
0
.025
.025
No Evidence Average Is Not 70
0
1.96
-1.96
Z
8
One-Tailed Z Test Thinking Challenge

• Youre an analyst for Ford. You want to find out
  if the average miles per gallon of Escorts is at
  least 32 mpg. Similar models have a standard
  deviation of 3.8 mpg. You take a sample of 60
  Escorts compute a sample mean of 30.7 mpg. At
  the .01 level, is there evidence that the miles
  per gallon is at least 32?

9
Solution Template

• H0
• H1
• ?
• n
• Critical Value(s)

Test Statistic Decision Conclusion
0
Z
10
One-Tailed Z Test Solution

• H0 ?X ? 32
• H1 ?X
• ? .01
• n 60
• Critical Value(s)

Test Statistic Decision Conclusion
X
?
?
?
30
7
32
.
x
Z
?
?
?
?
2
65
.
?
3
8
.
x
n
60
Reject
Reject at ? .01
.01
There Is Evidence Average Is Less than 32
Z
0
-2.33
11
Two-Tailed t TestThinking Challenge

• You work for the FTC. A manufacturer of
  detergent claims that the mean weight of
  detergent is 3.25 lb. You take a random sample
  of 64 containers. You calculate the sample
  average to be 3.238 lb. with a standard deviation
  of .117 lb. At the .01 level, is the
  manufacturer correct?

3.25 lb.
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Solution Template

• H0
• H1
• ?
• df
• Critical Value(s)

Test Statistic Decision Conclusion
t
0
13
Two-Tailed t Test Solution

• H0 ?X 3.25
• H1 ?X ? 3.25
• ? ? .01
• df ? 64 - 1 63
• Critical Value(s)

Test Statistic Decision Conclusion
X
?
?
?
3
238
3
25
.
.
x
t
?
?
?
?
82
.
S
117
.
n
64
Reject H
Reject H
Do Not Reject at ? .01
0
0
.005
.005
There is No Evidence Average Is Not 3.25
t
0
2.6561
-2.6561
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One-Tailed t Test Thinking Challenge

• Youre a marketing analyst for Wal-Mart.
  Wal-Mart had teddy bears on sale last week. The
  weekly sales ( 00) of bears sold in 10 stores
  was 8 11 0 4 7 8 10 5 8 3. At
  the .05 level, is there evidence that the average
  bear sales per store is more than 5 ( 00)?

15
Solution Template

• H0
• H1
• ?
• df
• Critical Value(s)

Test Statistic Decision Conclusion
t
0
16
One-Tailed t Test Solution

• H0 ?X ? 5
• H1 ?X 5
• ? .05
• df 10 - 1 9
• Critical Value(s)

Test Statistic Decision Conclusion
X
?
?
?
6
4
5
.
x
t
?
?
?
?
1
31
.
S
3
373
.
n
10
Reject
Do Not Reject at ? .05
.05
There Is No Evidence Average Is More than 5
t
0
1.8331