University of Phoenix Chapter 7 Coronavirus and Americas Economy Article HW Research an article on a current event that centers on a controversial issue wh

University of Phoenix Chapter 7 Coronavirus and Americas Economy Article HW Research an article on a current event that centers on a controversial issue where the two sides are claiming opposing views. Then, describe how you would analyze the situation to settle the issue if you were involved in this event. For example, if the article was about whether a proposed new law about gun control will reduce deaths, you may describe how you would use hypothesis testing to compare data from states where such laws exist. Or, if the article was about actions to take to reduce gas prices, you could talk about how you would use regression to figure out which factors affected prices at the pump the most. General discussions like “should marijuana be legal” or “do vaccines cause autism” are not appropriate. Pick a current and specific debate.

Please note that this discussion should be limited to how statistical analysis can be applied to current issues. This is not the place to champion a particular position on the issue you are discussing or get into an argument about the various sides of an issue. Remember, you are here to analyze, not proselytize.

Also note that the article you are citing must be discussing the opposing views on the issue. Do not introduce your own perspective on what is being disputed. For example if the article is about the new budget being passed but does not discuss any conflicts of opinion, it doesn’t qualify.

Please use the template below in your answers so everyone can easily follow your answers to all the questions (copy and paste to your post).

Use this template for your Unit 6 Discussion.

Summary of the article

Briefly describe the current event described in the article.

Central question

What does the article say about the issue being disputed? What are the conflicting points of view according to the article? Use direct quotes from the article to summarize the dispute and the opposing sides.

There has to be some specific issue in dispute at the center (do tax breaks increase spending, what impacts health care costs the most, etc.), and the sides have to be defending a particular position.

Do not use examples where the issue is based on opinions or morality. For example, “Should abortion be legal?” is largely a morality question and is not suitable for statistical analysis. Conducting a survey to ask people about their opinions is not the same as analyzing data and making conclusions- you still only have opinions.

Methodology

Explain which methodology you will apply. Provide the relevant details. Where will your data come from? How will the results from this methodology answer the question you described above?

If you are going to use forecasting, explain how you will do that (which methodology and why) and how you will measure your accuracy. How will the forecast settle the issue?

If you do a regression analysis, explain what the dependent and independent variables will be.

If you will do hypothesis testing, what will the null and alternative hypothesis be? Business Statistics
Tenth Edition
Ken Black
Chapter 7
Sampling and Sampling Distributions
Copyright ©2020 John Wiley & Sons, Inc.
Learning Objectives
1. Contrast sampling to census and differentiate among
different methods of sampling by assessing the
advantages associated with each.
2. Describe the distribution of a sample’s mean using the
central limit theorem, correcting for a finite population
if necessary.
3. Describe the distribution of a sample’s proportion using
the z formula for sample proportions.
Copyright ©2020 John Wiley & Sons, Inc.
2
7.1 Sampling (1 of 16)
Reasons for Sampling
• The sample can save money
• The sample can save time
• For given resources, the sample can broaden the scope
of the study
• Because the research process is sometimes destructive,
the sample can save product
• If accessing the population is impossible, the sample is
the only option
Copyright ©2020 John Wiley & Sons, Inc.
3
7.1 Sampling (2 of 16)
Reasons for Taking a Census
• Eliminate the possibility that by chance a randomly selected
sample may not be representative of the population
• For the safety of the consumer
• To benchmark data for future studies
Frame
• List, map, directory, or some other source used in the
sampling process to represent the population
• Also called the working population
Copyright ©2020 John Wiley & Sons, Inc.
4
7.1 Sampling (3 of 16)
Frame
• Overregistered: contains units that are not in the target
population
• Underregistered: does not contain some units that are in the
target population
Copyright ©2020 John Wiley & Sons, Inc.
5
7.1 Sampling (4 of 16)
Random Versus Nonrandom Sampling
• Random sampling: every unit of the population has the same
probability of being selected into the sample
• Nonrandom sampling: not every unit of the population has the
same probability of being selected into the sample
o
Generally NOT an appropriate technique for gathering data for
statistical analysis
Simple Random Sampling
• Each unit in the frame is numbered from 1 to N (the size of the
population)
• A random number table or generator is used to select n items into
the sample
Copyright ©2020 John Wiley & Sons, Inc.
6
7.1 Sampling (5 of 16)
Simple Random Sampling
Example: From the population frame of companies in Table 7.3, select a simple random
sample of six companies
• First, the companies were numbered from 1 to 30
TABLE 7.3: Numbered population of 30 Companies
01 Alaska Airlines
11 DuPont
21 Lubrizol
02 Alcoa
12 ExxonMobil
22 Mattel
03 Ashland
13 General Dynamics
23 Merck
04 Bank of America
14 General Electric
24 Microsoft
05 Boeing
15 General Mills
25 Occidental Petroleum
06 Chevron
16 Halliburton
26 JCPenney
07 Citigroup
17 IBM
27 Procter & Gamble
08 Clorox
18 Kellogg
28 Ryder
09 Delta Air Lines
19 Kroger
29 Sears
10 Disney
20 Lowe’s
30 Time Warner
Copyright ©2020 John Wiley & Sons, Inc.
7
7.1 Sampling (6 of 16)
Example
• From the table of random numbers (Table 7.1), two-digit numbers
are selected, discarding any that are over 30
• In the table of random numbers, the first two digits are 91, which
is unusable
• The second two digits are 56, also unusable, as is 74, the next two
digits
• The fourth set of two digits is 25, which corresponds with
Occidental Petroleum
Copyright ©2020 John Wiley & Sons, Inc.
8
7.1 Sampling (7 of 16)
TABLE 7.1: A Brief Table of Random Numbers
91567
42595
27958
30134
04024
86385
29880
99730
46503

18584
18845
49618
02304
51038
20655
58727
34914
63974
88720
82765
34476
17032
87589
40836
57491
16703
23167
49323
45021
33132
12544
41035
30405
83946
23792
14422
15059
45799
22716
19792
09983
74353
68668
30429
70735
25499
16631
35006
85900
07119
97336
71048
08178
77233
13916
47564
Copyright ©2020 John Wiley & Sons, Inc.
9
7.1 Sampling (8 of 16)
Example
• Continue moving across the rows until 6 two-digit numbers are
selected
• Sample will be:
o
(25) Occidental Petroleum
o
(27) Procter & Gamble
o
(01) Alaska Airlines
o
(04) Bank of America
o
(02) Alcoa
o
(29) Sears
Copyright ©2020 John Wiley & Sons, Inc.
10
7.1 Sampling (9 of 16)
Stratified Random Sampling
• Population is divided into nonoverlapping subpopulations (strata)
• Analyst selects a random sample from each
o
o
o
Can reduce sampling error, because sample will more closely match the population
More costly than a simple random sample
Strata are usually chosen based on available information about the population
• Within each group, there should be homogeneity
• Between each group, there should be heterogeneity
Copyright ©2020 John Wiley & Sons, Inc.
11
7.1 Sampling (10 of 16)
Stratified Random Sampling
• Proportionate stratified random sampling occurs when the
percentage of the sample taken from each stratum is proportionate to
the percentage that each stratum is within the whole population
o
o
Example: suppose voters are being surveyed in Boston and the sample is
being stratified by religion as Catholic, Protestant, Jewish, and others
If Boston’s population is 90% Catholic and if a sample of 1,000 voters is
taken, the sample would require inclusion of 900 Catholics to achieve
proportionate stratification
• Disproportionate stratified random sampling occurs when the
percentage of each stratum in the sample is different from the
percentage that each stratum is within the whole population
Copyright ©2020 John Wiley & Sons, Inc.
12
7.1 Sampling (11 of 16)
Systematic Sampling
• Every kth item is selected to produce a sample of size n from a population of
size N
k=
N
n
Example: A business analyst wanted to sample Texas manufacturers as part of a
management study.
• Wanted to sample 1,000 companies
• Frame – most recent edition of the Texas Manufacturers Register® which
listed 22,000 manufacturing companies in alphabetic order
 22, 000 
• The value of k is 
 = 22
1,
000


• Use random number table to choose the first element in the study
Copyright ©2020 John Wiley & Sons, Inc.
13
7.1 Sampling (12 of 16)
Cluster (or Area) Sampling
• Dividing population into nonoverlapping areas
• Clusters that are internally heterogeneous
o Example: states, cities
• If clusters are too large, a second set of clusters can be taken from
the initial cluster (two-stage sampling)
• Advantages: convenience, cost
• Disadvantages: may be less efficient than simple random
sampling if the elements of the cluster are similar
Copyright ©2020 John Wiley & Sons, Inc.
14
7.1 Sampling (13 of 16)
Nonrandom Sampling
• Any method that does not involve a random selection process
Convenience Sampling
• Selected for the convenience of the analyst
Judgment Sampling
• Chosen by the judgement of the analyst
o
o
Since the probability of an element being selected cannot be
determined, cannot determine sampling error
Can be biased due to systematic errors in judgment
Copyright ©2020 John Wiley & Sons, Inc.
15
7.1 Sampling (14 of 16)
Quota Sampling
• Population subclasses, such as age or gender, are used
as strata
• Can be useful if no frame is available for the population
• Can be less costly
• Nonrandom, and thus probabilities cannot be calculated
Copyright ©2020 John Wiley & Sons, Inc.
16
7.1 Sampling (15 of 16)
TABLE 7.4: Using Quota Sampling to Fill Quotas of Consumers by Age
Age Category
Quota
How Sample is Obtained
14–18 years old
70
Go to the nearest high school and survey willing
students as they leave school until you have surveyed
70 students
25–39 years old
30
Go to junior soccer matches and survey parents in the
stands until you have 30 surveys
Over 65 years old
40
Go to the activity center of a retirement community
and survey whomever will talk to you
Snowball Sampling
• Survey subjects are selected based on referral from other survey
respondents.
Copyright ©2020 John Wiley & Sons, Inc.
17
7.1 Sampling (16 of 16)
Sampling Error
• Occurs when the sample is not representative of the population
Nonsampling Error
• All other errors other than sampling error
o
o
o
o
o
o
o
Missing data
Recording errors
Measurement errors
Input processing errors
Analysis errors
Response errors
And many more!
Copyright ©2020 John Wiley & Sons, Inc.
18
7.2 Sampling Distribution of x bar (1 of 12)
Suppose that a small, finite population contains only N = 8 numbers:
54 55 59 63 64 68 69 70
• Distribution of the population data:
• Suppose that all possible samples of size n = 2 are taken from this
population
Copyright ©2020 John Wiley & Sons, Inc.
19
7.2 Sampling Distribution of x bar (2 of 12)
Population:
54 55 59 63 64 68 69 70
All possible samples of n = 2:
• Then take the means of all of the samples
(54, 54)
(55, 54)
(59, 54)
(63, 54)
(54, 55)
(55, 55)
(59, 55)
(63, 55)
(54, 59)
(55, 59)
(59, 59)
(63, 59)
(54, 63)
(55, 63)
(59, 63)
(63, 63)
(54, 64)
(55, 64)
(59, 64)
(63, 64)
(54, 68)
(55, 68)
(59, 68)
(63, 68)
(54, 69)
(55, 69)
(59, 69)
(63, 69)
(54, 70)
(55, 70)
(59, 70)
(63, 70)
(64, 54)
(68, 54)
(69, 54)
(70, 54)
(64, 55)
(68, 55)
(69, 55)
(70, 55)
(64, 59)
(68, 59)
(69, 59)
(70, 59)
(64, 63)
(68, 63)
(69, 63)
(70, 63)
(64, 64)
(68, 64)
(69, 64)
(70, 64)
(64, 68)
(68, 68)
(69, 68)
(70, 68)
(64, 69)
(68, 69)
(69, 69)
(70, 69)
(64, 70)
(68, 70)
(69, 70)
(70, 70)
Copyright ©2020 John Wiley & Sons, Inc.
20
7.2 Sampling Distribution of x bar (3 of 12)
Means of the samples:
54
54.5
56.5
58.5
59
61
61.5
62
54.5
55
57
59
59.5
61.5
62
62.5
56.5
57
59
61
61.5
63.5
64
64.5
58.5
59
61
63
63.5
65.5
66
66.5
59
59.5
61.5
63.5
64
66
66.5
67
61
61.5
63.5
65.5
66
68
68.5
69
61.5
62
64
66
66.5
68.5
69
69.5
62
62.5
64.5
66.5
67
69
69.5
70
Copyright ©2020 John Wiley & Sons, Inc.
21
7.2 Sampling Distribution of x bar (4 of 12)
Distribution of the means of the samples:
Copyright ©2020 John Wiley & Sons, Inc.
22
7.2 Sampling Distribution of x bar (5 of 12)
Distribution of the mean of the samples looks different
from the original distribution:
Copyright ©2020 John Wiley & Sons, Inc.
23
7.2 Sampling Distribution of x bar (6 of 12)
Similarly, the histogram of a Poisson distribution and its
samples are different:
Copyright ©2020 John Wiley & Sons, Inc.
24
7.2 Sampling Distribution of x bar (7 of 12)
The Central Limit Theorem
• If random samples of size n are repeatedly drawn from a population that
has a mean of μ and a standard deviation of σ, the sample means, x ,
are approximately normally distributed for sufficiently large sample sizes
(n ≥ 30), regardless of the shape of the population distribution. If the
population is normally distributed, the sample means are normally
distributed for any size sample.
• It can be shown that the mean of the sample means is the population mean:
x = 
• The standard deviation of the sample means (the standard error of the mean) is:
x =

n
Copyright ©2020 John Wiley & Sons, Inc.
25
7.2 Sampling Distribution of x bar (8 of 12)
Figure 7.9 Shapes of the Distributions of Sample Means for Three Sample Sizes
Drawn from Four Different Population Distributions
Copyright ©2020 John Wiley & Sons, Inc.
26
7.2 Sampling Distribution of x bar (9 of 12)
• If the sample size is greater than 30 or the population is normally distributed,
the sample means are normally distributed, and z scores can be used to
evaluate individual values
x −
z=

n
Example: Suppose the population mean expenditure per customer at a tire store is
$125 and the population standard deviation is $30. If a random sample of 40
customers is taken, what is the probability that the sample mean expenditure is
more than $133?
• Because the sample size is greater than 30, the central limit theorem can be
used, and the sample means are normally distributed
z=
x −

n
=
133 − 125
= 1.69
30
40
Copyright ©2020 John Wiley & Sons, Inc.
27
7.2 Sampling Distribution of x bar (10 of 12)
Example, continued:
• From the z distribution table, z = 1.69 gives a probability of .4545
• .5 −.4545 = .0455
• 4.55% of the time, a random sample of 40 customers from this population
would yield a sample mean expenditure of $133 or more when the population
mean is $125
Copyright ©2020 John Wiley & Sons, Inc.
28
7.2 Sampling Distribution of x bar (11 of 12)
Sampling from a Finite Population
• In cases of a finite population, a statistical adjustment must be
made to the z formula for sample means
z=
x −

n
N −n
N −1
• A rough rule of thumb is to use the finite population correction
factor when n  .05
N
• The correction factor reduces the size of the standard error of the
mean, because when the sample is large relative to the population,
the sample mean is less likely to vary from the population mean
Copyright ©2020 John Wiley & Sons, Inc.
29
7.2 Sampling Distribution of x bar (12 of 12)
TABLE 7.6: Finite Correction Factor for Some Sample Sizes
Population Size
2000
Sample Size
Value of Correction Factor
30(
Purchase answer to see full
attachment