Essentials of Modern Business Statistics (7e)
Essentials of Modern
Business Statistics (7e)
Anderson, Sweeney, Williams, Camm, Cochran
© 2018 Cengage Learning
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Chapter 8
Interval Estimation





Population Mean: s Known
Population Mean: s Unknown
Determining the Sample Size
Population Proportion
Big data and Interval estimation
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Margin of Error and the Interval Estimate
 A point estimator cannot be expected to provide the exact value of
the population parameter.
 An interval estimate can be computed by adding and subtracting a
margin of error to the point estimate.
Point Estimate +/- Margin of Error
 The purpose of an interval estimate is to provide information about
how close the point estimate is to the value of the parameter.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
Margin of Error and the Interval Estimate
The general form of an interval estimate of a population mean is
𝑥 + Margin of Error
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
 In order to develop an interval estimate of a population mean,
the margin of error must be computed using either:
• the population standard deviation s , or
• the sample standard deviation s
 s is rarely known exactly, but often a good estimate can be
obtained based on historical data or other information.
 We refer to such cases as the s known case.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
There is a 1 -  probability that the value of a sample
mean will provide a margin of error of 𝑧𝛼/2 𝜎𝑥 or less.
/2
/2
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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6
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
Interval Estimate of m
𝑥 ± 𝑧𝛼/2
where:
𝜎
𝑛
𝑥
is the sample mean
1 -  is the confidence coefficient
z/2
is the z value providing an area of /2 in the upper
tail of the standard normal probability distribution
s
is the population standard deviation
n
is the sample size
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
Values of z/2 for the Most Commonly Used Confidence Levels
Confidence
level

/2
Look-up Area
z/2
90%
.1
.05
.9500
1.645
95%
.05
.025
.9750
1.960
99%
.01
.005
.9950
2.576
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otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Meaning of Confidence
 Because 90% of all the intervals constructed using 𝑥 + 1.645𝜎𝑥 will
contain the population mean, we say we are 90% confident that the
interval 𝑥 + 1.645𝜎𝑥 includes the population mean m.
 We say that this interval has been established at the 90%
confidence level.
 The value .90 is referred to as the confidence coefficient.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
Example: Lloyds Department store
Each week Lloyds department store selects a simple random sample of
100 customers in order to learn about the amount spent per shopping
trip. The historical data indicates that the population follows a normal
distribution.
During most recent week, Lloyd’s surveyed 100 customers (n = 100)
and obtained a sample mean of 𝑥 = $82. Based on historical data,
Lloyd’s now assumes a known value of 𝜎 = $20. The confidence
coefficient to be used in the interval estimate is .95.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
Example: Lloyds Department store
95% of the sample means that can be observed are within + 1.96 𝜎𝑥 of
the population mean m. The margin of error is:
𝑧𝛼/2
𝜎
= 1.96
𝑛
20
100
= 3.92
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
Example: Lloyds Department store
Interval estimate of m is:
$82 + $ 3.92
or
$78.08 to $85.29
We are 95% confident that the interval contains the population mean.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
13
Essentials of Modern Business Statistics (7e)
Using Excel to construct a confidence interval - s Known
 Excel Formula Worksheet
Note: Rows 18-99
are not shown.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Using Excel to construct a confidence interval - s Known
 Excel Value Worksheet
Note: Rows 18-99
are not shown.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
Example: Lloyds Department store
Confidence level
Margin of Error
Interval estimate
90%
3.92
78.08 – 85.92
95%
3.29
78.71 – 85.29
99%
5.15
76.85 – 87.15
In order to have a higher degree of confidence, the margin of error and
thus the width of the confidence interval must be larger.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Known
Adequate Sample Size
 In most applications, a sample size of n ≥ 30 is adequate.
 If the population distribution is highly skewed or contains
outliers, a sample size of 50 or more is recommended.
 If the population is not normally distributed but is roughly
symmetric, a sample size as small as 15 will suffice.
 If the population is believed to be at least approximately normal,
a sample size of less than 15 can be used.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Unknown
 If an estimate of the population standard deviation s cannot be
developed prior to sampling, we use the sample standard deviation
s to estimate s .
 This is the s unknown case.
 In this case, the interval estimate for m is based on the t distribution.
 (We’ll assume for now that the population is normally distributed.)
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
t Distribution
 William Gosset, writing under the name “Student”, is the founder of
the t distribution.
 Gosset was an Oxford graduate in mathematics and worked for the
Guinness Brewery in Dublin.
 He developed the t distribution while working on small-scale
materials and temperature experiments.
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Essentials of Modern Business Statistics (7e)
t Distribution
 The t distribution is a family of similar probability distributions.
 A specific t distribution depends on a parameter known as the
degrees of freedom.
 Degrees of freedom refer to the number of independent pieces of
information that go into the computation of s.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
t Distribution
 A t distribution with more degrees of freedom has less dispersion.
 As the degrees of freedom increase, the difference between the t
distribution and the standard normal probability distribution
becomes smaller and smaller.
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Essentials of Modern Business Statistics (7e)
t Distribution
Comparison of the standard normal distribution with t distributions
having 10 and 20 degrees of freedom.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
t Distribution
 For more than 100 degrees of freedom, the standard normal z value
provides a good approximation to the t value.
 The standard normal z values can be found in the infinite degrees
row (labeled ∞ ) of the t distribution table.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
t Distribution
Selected values
from the t
distribution table
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Unknown
𝑥 ± 𝑡𝛼/2
where:
𝑠
𝑛
𝑥 = the sample mean
1 -  = the confidence coefficient
t/2 = the t value providing an area of /2 in the upper
tail of a t distribution with n - 1 degrees of freedom
s = the sample standard deviation
n = the sample size
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Unknown
Example: Credit card debt for the population of US households
The credit card balances of a sample of 70 households provided a
mean credit card debt of $9312 with a sample standard deviation of
$4007.
Let us provide a 95% confidence interval estimate of the mean credit
card debt for the population of US households. We will assume this
population to be normally distributed.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Unknown
 At 95% confidence,  = .05, and /2 = .025.
 t.025 is based on n - 1 = 70 - 1 = 69 degrees of freedom.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Unknown
Example: Credit card debt for the population of US households
𝑥 ± 𝑡.025
9312
4007
+ 1.995
70
𝑠
𝑛
= 9312 + 955
We are 95% confident that the mean credit card debt for the
population of US households is between $8357 and $10267.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Using Excel’s Descriptive Statistics Tool
Steps
Step 1: Click the Data tab on the Ribbon
Step 2: In the Analysis group click Data Analysis
Step 3: Choose Descriptive Statistics from the list of Analysis
tools
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otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Using Excel’s Descriptive Statistics Tool
Step 4: When the Descriptive statistics dialog box appears
• Enter Input Range
• Select Grouped by columns
• Select Labels in the first row
• Select Output range:
• Enter C1 in the output range box
• Select summary statistics
• Select confidence level for mean
• Enter 95 in the confidence level for mean box
• Click OK
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Using Excel’s Descriptive Statistics Tool
 Excel Worksheets
95% confidence interval
for credit card balances.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
31
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Mean: s Unknown
Adequate Sample Size
 Usually, a sample size of n ≥ 30 is adequate when using the
expression 𝑥 ± 𝑡𝛼/2 𝑠/ 𝑛 to develop an interval estimate of a
population mean.
 If the population distribution is highly skewed or contains
outliers, a sample size of 50 or more is recommended.
 If the population is not normally distributed but is roughly
symmetric, a sample size as small as 15 will suffice.
 If the population is believed to be at least approximately normal, a
sample size of less than 15 can be used.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
32
Essentials of Modern Business Statistics (7e)
Summary of Interval Estimation Procedures
for a Population Mean
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otherwise on a password-protected website or school-approved learning management system for classroom use.
33
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of a Population
Mean
 Let E = the desired margin of error.
 E is the amount added to and subtracted from the point estimate to
obtain an interval estimate.
 If a desired margin of error is selected prior to sampling, the sample
size necessary to satisfy the margin of error can be determined.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
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Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of a Population
Mean
 Margin of Error
𝐸 = 𝑧𝛼/2
𝜎
𝑛
 Necessary Sample Size
n=
(𝑧𝛼/2 )2 𝜎 2
𝐸2
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otherwise on a password-protected website or school-approved learning management system for classroom use.
35
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of a Population
Mean
 The Necessary Sample Size equation requires a value for the
population standard deviation s .
 If s is unknown, a preliminary or planning value for s can be used
in the equation.
1. Use the estimate of the population standard deviation
computed in a previous study.
2. Use a pilot study to select a preliminary study and use the
sample standard deviation from the study.
3. Use judgment or a “best guess” for the value of s .
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
36
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of a Population
Mean
Example: Cost of renting Automobiles in United States
A previous study that investigated the cost of renting automobiles in
the United States found a mean cost of approximately $55 per day for
renting a midsize automobile with a standard deviation of $9.65.
Suppose the project director wants an estimate of the population
mean daily rental cost such that there is a .95 probability that the
sampling error is $2 or less.
How large a sample size is needed to meet the required precision?
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
37
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of a Population
Mean
Example: Cost of renting Automobiles in United States
𝐸 = 𝑧𝛼/2
𝜎
=2
𝑛
At 95% confidence, z.025 = 1.96. Recall that s = 9.65.
𝑛=
(1.96)2 (9.65)2
(2)2
= 89.43 ⋍ 90
The sample size needs to be at least 90 mid size automobile rentals in
order to satisfy the project director’s $2 margin-of-error requirement.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
38
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Proportion
The general form of an interval estimate of a population proportion is:
𝑝 + Margin of Error
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
39
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Proportion
 The sampling distribution of 𝑝 plays a key role in computing the
margin of error for this interval estimate.
 The sampling distribution of 𝑝 can be approximated by a normal
distribution whenever np > 5 and n(1 – p) > 5.
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otherwise on a password-protected website or school-approved learning management system for classroom use.
40
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Proportion
Normal Approximation of Sampling Distribution of 𝑝
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
41
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Proportion
𝑝 ± 𝑧𝛼/2
𝑝(1 − 𝑝)
𝑛
where: 1 -  is the confidence coefficient,
z/2 is the z value providing an area of /2 in the upper tail
of the standard normal probability distribution, and
𝑝 is the sample proportion
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
42
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Proportion
Example: Survey of women golfers
A national survey of 900 women golfers was conducted to learn how
women golfers view their treatment at golf courses in United States.
The survey found that 396 of the women golfers were satisfied with
the availability of tee times.
Suppose one wants to develop a 95% confidence interval estimate for
the proportion of the population of women golfers satisfied with the
availability of tee times.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
43
Essentials of Modern Business Statistics (7e)
Interval Estimate of a Population Proportion
Example: Survey of women golfers
𝑝 ± 𝑧𝛼/2
𝑝(1 − 𝑝)
𝑛
where: n = 900, 𝑝 = 396/900 = .44, z/2 = 1.96
. 44 ±1.96
.44(1−.44)
900
= .44 ± .0324
Survey results enable us to state with 95% confidence that between 40.76% and
47.24% of all women golfers are satisfied with the availability of tee times.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
44
Essentials of Modern Business Statistics (7e)
Using Excel to construct a confidence interval
 Excel Formula and Value Worksheet
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
45
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of
a Population Proportion
Margin of Error
𝑝(1−𝑝)
𝑛
E = 𝑧𝛼/2
Solving for the necessary sample size n, we get
2
𝑧𝛼/2 𝑝 1 − 𝑝
𝑛=
𝐸2
However, 𝑝 will not be known until after we have selected the sample.
We will use the planning value p* for 𝑝.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
46
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of
a Population Proportion
Necessary Sample Size
𝑛=
𝑧𝛼/2
2 ∗
𝑝
1 − 𝑝∗
𝐸2
The planning value p* can be chosen by:
1. Using the sample proportion from a previous sample of the same or
similar units, or
2. Selecting a preliminary sample and using the sample proportion from this
sample.
3. Using judgment or a “best guess” for a p* value.
4. Otherwise, using .50 as the p* value.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
47
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of
a Population Proportion
Example: Survey of women golfers
Suppose the survey director wants to estimate the population
proportion with a margin of error of .025 at 95% confidence.
How large a sample size is needed to meet the required precision? (A
previous sample of similar units yielded .44 for the sample proportion.)
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
48
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of
a Population Proportion
Example: Survey of women golfers
E = 𝑧𝛼/2
𝑝∗ (1−𝑝∗ )
𝑛
= .025
At 95% confidence, z.0125 = 1.96. Recall that p* = .44.
2 ∗
𝑝
1 − 𝑝∗
1.96 2 (.44) .56
𝑛=
=
= 1514.5
2
2
𝐸
(.025)
A sample of size 1515 is needed to reach a desired precision of + .025 at 95%
confidence.
𝑧𝛼/2
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
49
Essentials of Modern Business Statistics (7e)
Sample Size for an Interval Estimate of
a Population Proportion
Note: We used .44 as the best estimate of p in the preceding
expression. If no information is available about p, then .5 is
often assumed because it provides the highest possible sample
size. If we had used p = .5, the recommended n would have
been 1537.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
50
Essentials of Modern Business Statistics (7e)
Implications of Big Data
 As the sample size becomes extremely large, the margin of error
becomes extremely small and resulting confidence intervals become
extremely narrow.
 No interval estimate will accurately reflect the parameter being
estimated unless the sample is relatively free of nonsampling error.
 Statistical inference along with information collected from other
sources can help in making the most informed decision.
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
51
Essentials of Modern Business Statistics (7e)
End of Chapter 8
© 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or
otherwise on a password-protected website or school-approved learning management system for classroom use.
52