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Doing Statistics for Business
Data, Inference, and Decision Making
Marilyn K. Pelosi
Theresa M. Sandifer
Chapter 9
Inferences: One
Population
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Doing Statistics for Business
Chapter 9 Objectives
 Hypothesis Test of the Population Mean,  :
Small Sample
 Hypothesis Test of the Population Variance,
2
 Hypothesis Test of the Population
Proportion, 
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Doing Statistics for Business
Chapter 9 Objectives (con’t)
 The Relationship Between Hypothesis
Testing and Confidence Intervals
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Doing Statistics for Business
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The Soda Machine
Test of Population Mean When 
Is Unknown
In Chapter 8 we looked at the hypothesis test to see if a soda machine was
correctly dispensing 32 oz of soda. The amount dispensed is assumed to
be normally distributed. The machine was not working properly if the
bottles were overfilled or underfilled. You observed the machine filling
30 bottles and collected the following data:
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The Soda Machine
Test of Population Mean When 
Is Unknown (con’t)
32.12
32.13
32.02
31.73
31.98
32.04
32.05
32.22
31.95
32.21
32.04
32.05
32.22
31.95
32.21
32.00
31.72
32.22
32.07
31.97
32.01
32.08
31.89
32.13
32.09
32.12
32.03
32.20
32.13
31.97
Is there any evidence to indicate that the machine is not filling the bottles
properly? Use  = 0.05.
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Doing Statistics for Business
Figure 9.1 Rejection
Region for a Lower-Tail
Test of 

Figure 9.2 Rejection
Region for an UpperTail Test of 

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Diameter of Washers
Lower-Tail Test of : Small Sample
Your company purchases washers. It is important that the diameter
of the hole not be more than 0.5 inch. If the hole in the center of the
washer is too large then your company will not be able to use the washer.
The diameters are assumed to be normally distributed. You have just
received a shipment of 10,000 of these washers. You decide to sample
20 to check to be sure that the diameters are not more than 0.5 inch, on the
average. Your measurements (in inches) are
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Diameter of Washers
Lower-Tail Test of : Small Sample (con’t)
0.5053
0.4711
0.4672
0.4672
0.5340
0.5098
0.4627
0.5642
0.5346
0.3767
0.4606
0.4800
0.5495
0.5745
0.3933
0.4606
0.4800
0.5495
0.5745
0.3933
Should you accept the shipment? Use  = 0.05
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Doing Statistics for Business
Figure 9.3
A Chi-Square
Distribution
Figure 9.4
Rejection Region for a
Two-Sided Test of the
Variance
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The Cereal Company
Testing the Variance
A cereal manufacturer wishes to test if the population variance of the
weight of the boxes is equal to 0.0500 oz2. A random sample of 20
boxes has a standard deviation of s = 0.25 oz. Use  = 0.05.
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Doing Statistics for Business
Lower-tail test of the
variance
Upper-tail test of the
variance
Figure 9.5 Rejection Regions for
One-sided Tests of the Variance
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Doing Statistics for Business
5-Step Hypothesis Testing Procedure
Step 1: Set up the null and alternative hypotheses.
Step 2: Define the test procedure.
Step 3: Collect the data and calculate the test statistic.
Step 4: Decide whether or not to reject the null
hypothesis.
Step 5: Interpret the statistical decision in terms of
the stated problem.
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Poll of Americans
Test of Proportion
She did it again. For the zillionith time, your mother casually asked
you when you are going to get married and you’ve been seething ever
since. How do you get it off your chest? These days, you might e-mail
her. The Pew Internet and American Life Project, based on a telephone
survey of 3,533 randomly selected adults recently (July, 2000)
calculated that 64 million of us e-mail our family members.
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Poll of Americans
Test of Proportion (cont’d)
Thirty-one percent of those who send family e-mail find it an easier
way to say frank or unpleasant things to their relatives.
Is there evidence that more than 30% of those who send family e-mail
use it to communicate unpleasant things? Use  = 0.05.
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The Soft Drink Company
One-Tail Test of Proportion
The Coca-Cola Company is interested in entering the fruit drink
market. Before bringing its new product, Fruitopia, to the market the
company wishes to be sure that it will capture more than 20% of the fruit
drink market. A survey of 1000 people shows that 230 respondents prefer
Fruitopia to other fruit drinks. Is there enough evidence to allow Coca
Cola to proceed with the new product? Use  = 0.05.
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Doing Statistics for Business
Discovery Exercise 9.1
Exploring the Connection Between
Confidence Intervals & Hypothesis
Testing
Part I
A recent survey is offering the first evidence that PCs are replacing TVs
as the primary source of home recreation, information, and entertainment.
The survey was conducted among 1200 homes nationwide. The average
computer user spends 9.5 hours per week in front of the PC but only 8
hours per week watching prime-time TV.
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Doing Statistics for Business
Discovery Exercise 9.1
Exploring the Connection Between
Confidence Intervals & Hypothesis
Testing (con’t)
Assume that the standard deviation of hours spent in front of a PC is 3
hours/week.
(a) Test the hypothesis that the average number of hours per week a
computer user spends in front of a PC is different from 8 hours.
Use  = 0.05.
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Doing Statistics for Business
Discovery Exercise 9.1
Exploring the Connection Between
Confidence Intervals & Hypothesis
Testing (con’t)
(b) Test the hypothesis that the average number of hours per week a
computer user spends in front of a PC is different from 8 hours.
Use  = 0.05.
( c) Is the value of 8 in the confidence interval you constructed in part
(b)?
(d) Did you reject the null hypothesis in part (a)?
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Doing Statistics for Business
Discovery Exercise 9.1
Exploring the Connection Between
Confidence Intervals & Hypothesis
Testing (con’t)
Part II
The Casual Businesswear Employee Survey was conducted to assess the
attitudes and behavior of white-collar employees whose companies allow
casual dress on some basis. The study was national in scope and the
sample size was 752 people. Of those sampled, 609 agree that allowing
casual dress improves morale.
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Doing Statistics for Business
Discovery Exercise 9.1
Exploring the Connection Between
Confidence Intervals & Hypothesis
Testing (con’t)
(a) Test the hypothesis that the proportion of white-collar employees who
agree that allowing casual dress improves morale is different from
80%. Use  = 0.05.
(b) Construct a 95% confidence interval for .
( c) Is the value of 0.80 in the confidence interval?
(d) Did you fail to reject the null hypothesis?
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Doing Statistics for Business
Discovery Exercise 9.1
Exploring the Connection Between
Confidence Intervals & Hypothesis
Testing (con’t)
Part III
Summarize. Based on these two situations, speculate how you would
complete the following statements:
If the value of the parameter being tested (the one in the null
hypothesis) is not in the confidence interval then I will ______________
the null hypothesis.
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Doing Statistics for Business
Discovery Exercise 9.1
Exploring the Connection Between
Confidence Intervals & Hypothesis
Testing (con’t)
If the value of the parameter being tested (the one in the null
hypothesis) is in the confidence interval then I will ______________
the null hypothesis.
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Doing Statistics for Business
Hypothesis Testing in KaddStat
KaddStat provides statistical functions that allow
you to perform hypothesis tests for both means
and proportions.
The basic steps are the same for each. The only
differences are the input that the user must supply.
We will give detailed directions for the small
sample hypothesis test for the mean. Once you
understand this procedure, the others are very
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similar.
Doing Statistics for Business
Small Sample Tests for the Population Mean in
KaddStat
1. From the Kadd menu choose Hypothesis Testing>One
Sample
2. Choose Population Mean using t
3. The dialog box shown on the next slide will open.
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Doing Statistics for Business
KaddStat Dialog Box
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Doing Statistics for Business
Three Main Parts of the Dialog Box
1. Null Hypothesis- input the value of the hypothesized mean 5 seconds.
2. Alternative Hypthesis -identify the form of the alternative
hyothesis- click the radio button next to Not equal
3. Data/user- indicate that you have the raw data so click the
button labeled Input Range. Click on Header Row
Included if your data range is labeled with a variable
name.
4. Indicate where you want the results to be located.
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Doing Statistics for Business
Completed KaddStat Dialog Box
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Doing Statistics for Business
Chapter 9 Summary
In this chapter you have learned:
 How to do a hypothesis test of the:
Population Mean
Population Variance
Population Proportion
 The differences in the test are in the rejection
regions, and the calculations of the test statistic.
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Doing Statistics for Business
Chapter 9 Summary (con’t)
 For a test of the Population Mean, use a Z test if
the population standard deviation is known;
otherwise use a t test.
 For a test of the Population Variance, use a chi-
square test
 For a test of Proportions use a Z test.
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Doing Statistics for Business
Chapter 9 Summary (con’t)
 In any hypothesis test the rejection region and the
final decision depend on the value of . You can
alter the outcome of the test by adjusting the value
of .
 Use p values to handle potential unethical uses of
hypothesis testing and to provide management
with more information.
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