Midterm2–PracticeExercises 11. The amoun.docx

Midterm 2 – Practice Exercises
1
1. The amount of material used in making a custom sail for a
sailboat is normally
distributed with a standard deviation of 64 square feet. For a
random sample of 15
sails, the mean amount of material used is 912 square feet.
Which of the following
represents a 99% confidence interval for the population mean
amount of material
used in a custom sail?
A. 912 ± 49.2
B. 912 ± 42.6
C. 912 ± 44.3
D. 912 ± 46.8
2. The number of beverage cans produced each hour from a
vending machine is
normally distributed with a standard deviation of 8.6. For a
random sample of 12
hours, the average number of beverage cans produced was
326.0. Assume a 99%
confidence interval for the population mean number of beverage
cans produced
per hour. Calculate the margin of error of the 99% confidence
interval.

A. 1.85
B. 3.60
C. 6.41
D. 10.56
3. The number of beverage cans produced each hour from a
vending machine is
normally distributed with a standard deviation of 8.6. For a
random sample of 12
hours, the average number of beverage cans produced was
326.0. Assume a 99%
confidence interval for the population mean number of beverage
cans produced
per hour. Find the upper confidence limit of the 99% confidence
interval.
A. 340.25
B. 325.98
C. 319.59
D. 332.41
4. If we change a 95% confidence interval estimate to a 99%
confidence interval
estimate, we can expect
A. the size of the confidence interval to increase
B. the size of the confidence interval to decrease
C. the size of the confidence interval to remain the same
D. the sample size to increase

2
5. If a sample has 20 observations and a 90% confidence
estimate for µ is needed,
the appropriate t‐score is:
A. 2.120
B. 1.746
C. 2.131
D. 1.729
6. We are interested in conducting a study to determine what
percentage of voters
would vote for the incumbent member of parliament. What is
the minimum size
sample needed to estimate the population proportion with a
margin of error of
0.07 or less at 95% confidence?

A. 200
B. 100
C. 58
D. 196
7. The sample size needed to provide a margin of error of 2 or
less with a 0.95
confidence coefficient when the population standard deviation
equals 11 is
A. 10
B. 11
C. 116
D. 117
8. The manager of the local health club is interested in
determining the number of
times members use the weight room per month. She takes a
random sample of 15
members and finds that over the course of a month, the average
number of visits
was 11.2 with a standard deviation of 3.2. Assuming that the
monthly number of
visits is normally distributed, which of the following represents
a 95% confidence
interval for the average monthly usage of all health club
members?
A. 11.2 ± 1.74
B. 11.2 ± 1.77

C. 11.2 ± 1.62
D. 11.2 ± 1.83
3
9. The supervisor of a production line believes that the average
time to assemble an
electronic component is 14 minutes. Assume that assembly time
is normally
distributed with a standard deviation of 3.4 minutes. The
supervisor times the
assembly of 14 components, and finds that the average time for
completion is
11.6 minutes. What are the appropriate null and alternative
hypotheses?
A. H0 : µ ≥ 14 and H1: µ < 14
B. H0 : µ ≤ 14 and H1: µ > 14
C. H0 : µ = 14 and H1: µ ≠ 14
D. H0 : µ ≠ 14 and H1: µ = 14
10. The supervisor of a production line believes that the average
time to assemble an
electronic component is 14 minutes. Assume that assembly time
is normally
distributed with a standard deviation of 3.4 minutes. The

supervisor times the
assembly of 14 components, and finds that the average time for
completion is
11.6 minutes. What are the appropriate null and alternative
hypotheses? Which of
the following statements is most accurate?
A. fail to reject the null hypothesis at α ≤ 0.10
B. reject the null hypothesis at α = 0.025, but not at α = 0.05
C. reject the null hypothesis at α = 0.05, but not at α = 0.01
D. reject the null hypothesis at α = 0.01
11. For a one-tailed hypothesis test (upper tail) the p-value is
computed to be 0.034. If
the test is being conducted at 95% confidence, the null
hypothesis
A. could be rejected or not rejected depending on the sample
size
B. could be rejected or not rejected depending on the value of
the mean of the
sample
C. is not rejected
D. is rejected
12. In a two-tailed hypothesis test the test statistic z is
determined to be –2.5. The p-
value for this test is
A. −1.25
B. 0.4938
C. 0.0062

D. 0.0124
13. An accountant claims to be able to complete a standard tax
return in under an
hour. For a random sample of 24 tax returns, the accountant
averaged 63.2
minutes with a standard deviation of 7.7 minutes. What is the
test statistic for this
test?
A. Z = 2.04
B. t = 1.79
C. t = 2.04
D. Z = 1.79
4
return in under an
averaged 63.2
minutes with a standard deviation of 7.7 minutes. What are the
appropriate null
and alternative hypotheses?
A. H0 : µ = 60 and H1 : µ ≠ 60
B. H0 : µ = 60 and H1 : µ > 60
C. H0 : µ = 60 and H1 : µ < 60
D. H0 : µ > 60 and H1 : µ ≤ 60

return in under an
averaged 63.2
minutes with a standard deviation of 7.7 minutes. What is the
most accurate
estimate of the p‐value?
A. 0.025 < p‐value < 0.05
B. 0.01 < p‐value < 0.025
C. 0.05 < p‐value < 0.10
D. p‐value < 0.01
16. Salary information regarding male and female employees of
a large company is
shown
Male Female
Sample Size (n) 64 36
Sample Mean Salary (in 1,000) 44 41
Population Variance (σ2 ) 128 72
We want to test whether the mean salary of female (µF) is
bigger than mean salary
of male (µM). What are the appropriate null and the alternative
hypotheses?
A. H0: µF = µM , HA: µF ≠ µM
B. H0: µF > µM , HA: µF ≤ µM
C. H0: µF < µM , HA: µF ≥ µM
D. H0: µF= µM , HA: µF>µM

5
17. Salary information regarding male and female employees of
a large company is
shown
Male Female
Sample Size (n) 64 36
Sample Mean Salary (in 1,000) 44 41
Population Variance (σ2) 128 72
We want to test whether the mean salary of female (µF) is
bigger than mean salary
of male (µM). What is the test statistic?
A. 1.75
B. 2.0

C. 1.5
D. 1.25
18. Test scores on a standardized test from samples of students
from two universities
are given below.
A B
Sample size 28 41
Average test score 84 82
Variance 64 100
90% confidence interval estimate for the difference between the
test scores of the
two universities:
A. 0.72 to 4.94
B. -1.63 to 5.63
C. -2.91 to 3.55
D. -0.88 to 6.17
6
Answer Key
1. B
2. C

3. D
4. A
5. D
6. D
7. D
8. C
9. C
10. D
11. D
12. D
13. C
14. B
15. A
16. B
17. C
18. D
COVID-19 Optional Assignment
Ryder Burliss
3034079559
Word Count My Essay: 1511
Word Count Peer Review 1: XXX
Prompt 4: VSL
COVID-19: The Value Of A Life
The current Pandemic, Covid-19 has affected everyone around
the globe. Thankfully, our

medical staff, doctors and nurses are working tirelessly day and
night to fight back against the
virus as it threatens thousands of lives and claims hundreds,
everyday. But the fact is, not
everyone can be saved. Our health heros are being faced with an
unethical decision, who gets
treatment and hopefully survives, and who doesn’t, leaving their
lives at the mercy of the virus.
As the crisis continues, during a press conference, New York
Governor, Andrew Cuomo
states, “You cannot put a value on human life.” However, in
order to make decisions on how
many resources are spent and distributed to reduce mortality
risks and death, conventional
estimates of the Value of Statistical Life, or VSL are used. The
VSL can be defined as how much
of your income you would pay, or economically speaking one's
(Willingness To Pay, WTP) to
reduce your risk and avoid fatality. The VSL is commonly used
in cost-benefit analysis when
comparing positive and negative aspects of a particular policy.
Graphically, this can be shown as
the slope along an indifference curve showing different bundles
that the consumer is indifferent

to choosing because the same utility is maintained at each point
along the curve.
In this pandemic, although it is unethical in normal
circumstances, I argue that the VSL
of younger people is much higher than the elderly’s. One's
willingness to pay to avoid risking
death depends primarily on age combined with one’s
vulnerability to diseases and whether or not
1
https://www.nationalreview.com/corner/yes-we-can-love-our-
elderly-too-and-must/
https://www.nationalreview.com/corner/yes-we-can-love-our-
elderly-too-and-must/
https://chds.hsph.harvard.edu/valuing-covid-mortality-risks/
https://www.researchgate.net/figure/VSL-is-the-slope-of-the-
individuals-indifference-curve-at-current-wealth-w-and-
survival_fig3_337876160
one has health complications that would make them more
susceptible to having complications
with the virus such as asthma. With this being said, VSL in this
pandemic is also influenced by
an individual's personal wealth which would undoubtedly affect
their WTP for survival.
The Value of Statistical Life, as discussed in lecture is a
hedonic analysis where the

amenity is the risk of death. Although hedonic analysis is a
revealed preference method,
environmental economist Alan Krupnick claims that two
methodical approaches to calculate
VSL are revealed preferences, which is a monetary tradeoff, and
stated preferences which is a
more hypothetical method. Revealed preference methods include
observations and statistical
analysis which differs from stated preferences that include
surveys and questions rather than
money to elicit people’s preferences regarding their WTP to
reduce risk of death. As a branch of
revealed preference methods, hedonic wage analysis leans
towards the human capital approach
to VSL and does not necessarily poll the group that is not
working, leaving them at a higher risk.
This coincides with the coronavirus pandemic because those not
working include most of the
elderly population who are also at a higher risk to catch the
virus and not survive. During this
pandemic the VSL of older people in comparison to younger
people proves to be lower as
younger people are given medical attention.
However, Alan Krupnick argues that VSL is an inappropriate

term used in this pandemic
because there aren’t clear society-wide trade-offs. However,
there are trade-offs but they are
certainly morally fraught. Such as, the Lieutenant Governor of
Texas states he would be willing
to give up his life for his grandchildren’s future economic
benefit and also suggests many others
would be too. I argue against Alan Krupnick that the VSL is a
necessary term used during this
crisis in order to appropriately allocate limiting resources. Also,
I argue there are in fact society-
2
https://www.resourcesmag.org/resources-radio/value-statistical-
life-and-coronavirus-alan-krupnick/
https://nymag.com/intelligencer/2020/03/dan-patrick-seniors-
are-willing-to-die-to-save-economy.html
wide tradeoffs such as those essential workers on the front lines
risking contracting the virus by
doing their job to help the community, as well as medical
workers having to choose whom to
save based on who has more life in them which certainly affects

society as a whole.
In attempting to place an economic value on one's willingness
to pay for life, moral
quandaries are being disputed by governments in every country.
As every country handles this
pandemic differently, we are all human and deciding who
should be saved and who should not is
unethical but necessary in these harrowing times. Reports from
Belgium include a ninety year
old woman, Suzanne Holylaerts who was first admitted to the
hospital for lack of appetite and
shortness of breath. Later she was diagnosed with the novel
coronavirus. While in isolation,
Suzanne told the doctors, “I don’t want artificial respiration.
Save it for younger patients. I
already had a good life.”. On March 22 Suzanne died,
sacrificing her life for those who are
younger. She deliberately chose a lower VSL in comparison to
those who are younger.
In other countries such as Italy, older people weren’t given the
choice to value younger
lives as more important than their own and the decision had to
be made by doctors. During this
profoundly grim time in Italy and other countries, doctors are

advised to focus their care on
younger patients who are more likely to survive while the older,
sicker patients are left to die.
Conventional estimates of the VSL are used here to decide that
the limited resources of medical
attention is distributed to the younger patients with higher
resilience and potential for survival.
With medical attention being a primary limiting resource in this
spiraling crisis of the
virus, having it allocated to those with lower risk of
complications supports my claim that VSL is
higher for those who are younger and stronger. While, the older
more susceptible patients during
this crisis are given a lower VSL without a choice as medical
professionals are being asked to
3
https://www.wsbtv.com/news/trending/coronavirus-90-year-old-
with-covid-19-says-no-ventilator-said-keep-it-younger-
ones/OLIN2MUR4BBMLDBRZOXTMIWPDE/
https://www.mirror.co.uk/news/world-news/coronavirus-grim-
advice-italian-doctors-21679627
prioritize their care to more adolescents, because as grimly as it
sounds, they have a much higher
chance of survival.

Economists and analysts have started asking a studded question
with moral and ethical
landmines about how much economic decline can we withstand
as a country in order to protect
public health .As this question attempts to be answered, a VSL
must be consulted. The value of
statistical life of doctors and other medical staff on the
frontlines of the epidemic, risking their
lives to save others I would assume to be quite low. I would
argue the VSL of our medical
professionals at this time is similar to men and women joining
the army because they are
deliberately choosing to risk their lives for others.
As Trump nearly threatens to open the economy up rather than
prioritizing public health,
healthcare workers could take the brunt of this decision.
Statistician and health economist,
Howard Steven Friedman, tells us that this dilemma involves
divulging a price-tag for a human
life, a VSL. The development of this price-tag is influenced by
human rights, economics,
philosophy, law, science. The numerical value says a lot about
what is prioritized in our country.

Also impacting the wellbeing of our healthcare workers are
government regulations that have
been put in to keep society safe and limit the decisions of who
gets to survive.
Although citizens continue to fight government restrictions,
such as social distancing and
the stay-at-home order, society as a whole feels the
repercussions. Countless posts on social
media and in the news picture doctors with masks, goggles,
holding up signs in gloved hands that
say “We stay here for you. Stay home for us”. There have even
been protests such as in Colorado
of people claiming their independence is being taken as
government restrictions remain and
strength amidst the chaos of the outbreak.
4
https://www.marketplace.org/2020/04/23/how-much-is-a-
human-life-worth/
https://i.dailymail.co.uk/1s/2020/03/24/11/26334158-8145927-
Australian_doctors_have_joined_the_global_effort_to_call_for_
peo-a-2_1585048087199.jpg
Although government restrictions have taken a toll on civil
liberties that we Americans

stand for, I argue it is wildly rational considering those who are
putting their lives on the line to
save us. Many writers and journalists are comparing these grim
times to war times as our rights
are limited. Obtaining food becomes a stressor and involves
risk, anxiety overwhelms the nation
as well as on a global scale. Unfortunately, President Trump
continues to make poor decisions
such as continually calling the pandemic the “Chinese virus”
which encourages racism against
Asian citizens.
Poor decisions may even be made in the hospitals as Ziod
Obermyer, acting Associate
Professor of Health Policy and Management at University Of
California Berkeley, suggests.
Obermeyer mentions in a Berkeley Conversation that there are
pitfalls in using numerical data
and algorithms in the allocation of healthcare resources during
the COVID-19 pandemic.
Obermeyer suggests that as limited health resources are
allocated towards the younger, healthier
patients who are more likely to survive, not only promotes
disparities, but may not be the

smartest move. If they are more likely to survive, the resources
such as respirators should be
allocated to those who need it the most.
Although disputes regarding the ethicality and appropriateness
of the Value of Statistical
Life’s usage during the Covid-19, it is still being implemented.
This is shown by essential
workers still going to work, potentially trading off their health
and safety to benefit society, as
well as traumatic decisions being made in hospitals. The VSL is
proven to be higher for younger,
stronger members of society in comparison to older, less
healthy ones in the case of the
pandemic because they are the ones where the limited health
resources are allocated.
5
https://news.berkeley.edu/2020/04/21/understanding-and-
seeking-equity-amid-covid-19/
Optional Assignment for EEP101/ECON125
Spring 2020
James Sallee

This assignment asks you to write a short essay applying key
concepts of the class to COVID-19.
COVID-19 is not quite a classical environmental problem, but it
shares the same basic features
of many environmental problems and thus serves as a potential
illustration (and perhaps test)
of many of the core ideas in the course.
Requirements:
• Write an essay answering the prompts below. The essay must
be between 1500 and
2000 words.
• Each essay will be sent randomly to another student for peer
review. (This will not be
anonymous.) Peers will write comments/critiques of your essay.
Each comment/critique
must be between 300 and 400 words.
• To get credit for the assignment, you must (a) write your
essay, (b) complete a peer
review and (c) follow the formatting instructions below to turn
in your essay and peer
review in one file.
Grading: I will review the submissions and assign a score out of
100. If you choose to participate
your final score in the class will whichever is higher of: (a)
your original letter grade, or (b) the
letter grade you would have earned given the established curve
if your COVID-19 assignment
counted for 20% of your grade, while the remaining material
counted for only 80%.

That is, I will count the COVID-19 assignment as 20% of your
grade, changing the weight on the
remaining material, unless it somehow hurts you (which is not
likely).
I will determine the curve and letter grades before accounting
for any optional assignments to
ensure that the letter grade of those not participating are
unaffected by the assignment.
Due date:
You must submit your initial essay on the last day of class, F
May 1.
You will then be randomly assigned someone’s report to
referee. You will need to turn in your
assignment with your referee item during RRR week on F May
8.
Formatting: Your essay must have the following information at
the top as a header that looks
like this:
COVID-19 Optional Assignment
[Your Name]
[Your Student ID]
Word Count My Essay: XXXX
List the prompt number and title that you choose: I.e.,

Prompt 2: Regulation
[Your essay here.]
If you answer more than one prompt, repeat this structure:
Prompt 4: VSL
[Your essay here.]
…repeat as needed
Peer Review: [Name of Student I reviewed]
[Your peer review comments here]
Prompts: Below are several prompts. You may choose to
respond to only one, or several. You
are free to agree, elaborate and expand. And you are equally
free to disagree and explain why.
You are to be graded on the quality and rigor of your argument,
not on whether you argue a
particular answer. You are more than welcome to reject the
validity of these concepts to the
present health crisis; I am interested in thinking about COVID-
19 as a “test” of the relevance of
our core policy ideas to the present problem.

If you have a different idea that is clearly related to the content
of the course, you may write
about that idea.
Hypothetical infection tax: Suppose it were possible to map
every time someone infects
another person. If that were possible, then we could simply levy
a tax such that every time
someone infects another person, they have to pay a tax.
1. Pigouvian prescription: If we could administer the
hypothetical infection tax, we should
implement such a tax, and that would restore market efficiency.
That is, if such a tax
were imposed, then people would choose behaviors that
efficiently balance benefits
against the costs of infecting others.
2. Regulation: To impact behavior, the main activity of
governments has been to shut
down parts of the economy, impose restrictions on group sizes
and meeting places, and
add other restrictions via shelter in place orders. These policies
are analogous to
traditional “command and control” regulations and they are
inefficient as compared to
the hypothetical infection tax.
3. Second-best policies: The hypothetical infection tax is not
feasible, but what is feasible
is for law enforcement to issue fines for violations of local
shelter in place rules. Explain
what the Diamond model implies about the second-best fine for

violating a shelter in
place order. Are the insights from the Diamond model likely to
be substantively
important in the real world?
4. Second-best policies II: Explain whether or not fines for
violation of shelter in place
regulations are a good substitute policy for the hypothetical
infection tax.
5. VSL: When deciding what policies are worth pursuing,
government actors and the public
are implicitly making judgments about how many resources to
spend to try to save lives.
It is reasonable to use conventional estimates of the VSL when
making these judgments.
6. Public goods: A better model for understanding COVID-19 is
public goods. In this view,
everyone can contribute to a public good via hygiene and social
distancing, etc. The
public good model suggests that relying on such voluntary
contributions will lead to an
inefficient outcome, and thus policy intervention is needed.

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