1. Describe a Time Spirituality was Important in your Life or that of Someone You Love or Cared for (E.G., Family Member, Friend, Patient). Why was it Meaningful in that Situation? Life has its dull and challenging moment that stretches humanity to take a step back and take a personal reflection driving one to a mindful, spiritual sensation. Spirituality gives people a feeling of hope, calmness, compassion, and gratitude. Spirituality can be achieved through prayer and meditation, among other culturally acceptable traditions (De Blot, 2011). In life, I have come across moments when my spiritualty was challenged, that of family and close friends and family. Back in 2017, my uncle was driving back from work late at night, but he was involved in a greasy road accident. The accident was fatal as he was taken to the hospital unconscious, and he remained in a coma state for over two weeks. I come from a tight family where we keep close relations with my grandparents, aunts, and uncles. We have dinners and family gatherings, often with all present. My uncle's accident was a challenge to everyone, especially to his young family of two. As he lay in the hospital unconscious, our family comes together in prayer every Sunday afternoon in my auntie's house. We all wanted him to recover and go home someday. In silence and gathering, we turned to God in worship and prayers seeking hope and healing over my uncle. I consider this a time when our family spirituality was tested, but we never gave up, because we are a strong Christian family that believes in God's love, grace, and protection. We also believe that through prayer and a strong belief in God, my uncle recovered and went home. 2. What would you do if a Patient Asked You to Pray with them or Read the Bible or another Holy Book He/She Might Have at the Bedside? According to De Blot (2011), spirituality and religion are two different things, but they both thrive on the existence of each. Unlike religion, spirituality is a personal affair that does not relies on groups of people's beliefs to thrive. As a spiritual’s person, I would be willing to read any scripture with a patient despite the difference in religions. I would never feel offended and show any kind of resistance because spirituality a sacred path that people seek purpose and meaning of self, others, and nature. If reading the scripture together with a Muslim patient gives them hope, which attributes to a quick recovery, then I will oblige. 3. There is Something Called Scripting, which is having Something Written and Memorized for Difficult Situations. Write a Prayer or Spiritual Message You Could Use in the in the above Situation. Explain why you chose those words. "Dear God, thank you for a new day and breathe of life. As we cruise through the day, grant me a favor, safety, good health, and abundance of your love and blessing. Allow positivity and wisdom to follow through the day and protect my family and me from any form of evil. Grant ...

1. 1. Describe a Time Spirituality was Important in your Life or
that of Someone You Love or Cared for (E.G., Family Member,
Friend, Patient). Why was it Meaningful in that Situation?
Life has its dull and challenging moment that stretches
humanity to take a step back and take a personal reflection
driving one to a mindful, spiritual sensation. Spirituality gives
people a feeling of hope, calmness, compassion, and gratitude.
Spirituality can be achieved through prayer and meditation,
among other culturally acceptable traditions (De Blot, 2011). In
life, I have come across moments when my spiritualty was
challenged, that of family and close friends and family. Back in
2017, my uncle was driving back from work late at night, but he
was involved in a greasy road accident. The accident was fatal
as he was taken to the hospital unconscious, and he remained in
a coma state for over two weeks.
I come from a tight family where we keep close relations with
my grandparents, aunts, and uncles. We have dinners and famil y
gatherings, often with all present. My uncle's accident was a
challenge to everyone, especially to his young family of two. As
he lay in the hospital unconscious, our family comes together in
prayer every Sunday afternoon in my auntie's house. We all
wanted him to recover and go home someday. In silence and
gathering, we turned to God in worship and prayers seeking
hope and healing over my uncle. I consider this a time when our
family spirituality was tested, but we never gave up, because we
are a strong Christian family that believes in God's love, grace,
and protection. We also believe that through prayer and a strong
belief in God, my uncle recovered and went home.
2. What would you do if a Patient Asked You to Pray with them
or Read the Bible or another Holy Book He/She Might Have at
the Bedside?
According to De Blot (2011), spirituality and religion are two
different things, but they both thrive on the existence of each.

2. Unlike religion, spirituality is a personal affair that does not
relies on groups of people's beliefs to thrive. As a spiritual’s
person, I would be willing to read any scripture with a patient
despite the difference in religions. I would never feel offended
and show any kind of resistance because spirituality a sacred
path that people seek purpose and meaning of self, others, and
nature. If reading the scripture together with a Muslim patient
gives them hope, which attributes to a quick recovery, then I
will oblige.
3. There is Something Called Scripting, which is having
Something Written and Memorized for Difficult Situations.
Write a Prayer or Spiritual Message You Could Use in the in the
above Situation. Explain why you chose those words.
"Dear God, thank you for a new day and breathe of life. As we
cruise through the day, grant me a favor, safety, good health,
and abundance of your love and blessing. Allow positivity and
wisdom to follow through the day and protect my family and me
from any form of evil. Grant healing to those in need and
restore hope to those in defeat. In Jesus' name, Amen."
Life brings us a bounty of good, bad, so we all need peace,
hope, and God. We need a higher power of guidance to
overcome harsh destinies, remain at peace, and make reasonable
judgments (Luhrmann & Morgain, 2012). All we need at the end
of the day is to count our blessing in joy and calmness. My
scripted prayer above helps attract the higher power in my daily
doings, invoking the spirit of healing, happiness, and bounty,
and introducing calmness in my everyday life. I begin my
prayers by showing gratitude for what I have then sought God's
favor in a new day. We all live in fear of bad things, so I seek
the higher power to provide and give safety. The prayer keeps
me hopeful for a good day.
References
De Blot, P. (2011). Religion and spirituality. In Handbook of
spirituality and business (pp. 11-17). Palgrave Macmillan,

3. London.
https://link.springer.com/chapter/10.1057%2F9780230321458_2
Luhrmann, T. M., & Morgain, R. (2012). Prayer as inner sense
cultivation: An attentional learning theory of spiritual
experience. Ethos, 40(4), 359-389.
https://www.researchgate.net/publication/260139832_Prayer_as
_Inner_Sense_Cultivation_An_Attentional_Learning_Theory_of
_Spiritual_Experience
Homework 2
Due: before 12:00 pm (noon) on Tuesday, March 30. Please do
not include your name on your write-up, since
these documents will be reviewed by anonymous peer graders.
For probability derivations, show your work and/or explain your
reasoning. Do not include your raw R
code in your write-up unless we explicitly ask for it. You will
submit your R script as a separate
document to the write-up itself. On Canvas, you will see two
assignments pages corresponding to Homework
2: (1) to upload your write-up PDF file and (2) to upload the R
script that you used to generate your
write-up. Your write-up is what will be peer graded. The R
script will not be graded, but you must submit it
to receive credit on the write-up.
If you use tables or figures, make sure they are formatted
professionally. Figures and tables should have
informative captions. Numbers should be rounded to a sensible
number of digits (you’re at UT and therefore
a smart cookie; use your judgment for what’s sensible
depending on the level of precision that is appropriate
for the problem context).

4. Problem 1 - NHANES
The American National Health and Nutrition Examination
Surveys (NHANES) are collected by the US
National Center for Health Statistics, which has conducted a
series of health and nutrition surveys since
the early 1960s. Since 1999, approximately 5,000 individuals of
all ages are interviewed each year. For this
problem you will need to install the NHANES package in
RStudio with a built-in data frame called NHANES.
library(NHANES)
library(mosaic)
data(NHANES)
Part A: Create a histogram for the distribution of SleepHrsNight
for individuals aged 18-22 (inclusive) via
the bootstrap. Use at least 10000 iterations. Include the plot and
report the mean sleep hours for this age
group. Optional: how does your sleep compare?
Part B: Now we want to build a confidence interval for the
proportion of women we think are pregnant at
any given time. Bootstrap a confidence interval with 10000
iterations. Include in your write-up a histogram
of your simulation results, along with a 95% confidence interval
for the proportion. To speed things up, you
can use this code to subset the NHANES data frame to one with
only women. Let’s get rid of the N/A values
for our variable of interest (PregnantNow) in our filtered data
frame:
NHANES_women <- NHANES %>%
filter(Gender=="female",
!is.na(PregnantNow)

5. )
Problem 2 - Iron Bank
The Securities and Exchange Commission (SEC) is
investigating the Iron Bank, where a cluster of employees
have recently been identified in various suspicious patterns of
securities trading. Of the last 2021 trades, 70
were flagged by the SEC’s detection algorithm. Trades are
flagged periodically even when no illicit market
activity has taken place. For that reason, the SEC often
monitors individual and institutional trading but
does not investigate detected incidents that may be consistent
with random variability in trading patterns.
SEC data suggest that the overall baseline rate of suspicious
securities trades is 2.4%.
Are the observed data (70 flagged trades out of 2021) consistent
with the SEC’s null hypothesis that, over the
long run, securities trades from the Iron Bank are flagged at the
same baseline rate as that of other traders?
Use Monte Carlo simulation (with at least 100000 simulations)
to calculate a p-value under this null hypothesis.
Include the following items in your write-up:
1
• the null hypothesis that your are testing;
• the test statistic you used to measure evidence against the null
hypothesis;
• a plot of the probability distribution of the test statistic,

6. assuming that the null hypothesis is true;
• the p-value itself;
• and a one-sentence conclusion about the extent to which you
think the null hypothesis looks plausible
in light of the data. This one is open to interpretation! Make
sure to defend your conclusion.
Problem 3 - Armfold
A professor at an Australian university ran the following
experiment with her students in a data science
class. Everyone in the class stood up, and the professor asked
everyone to fold their arms across their chest.
Students then filled out an online survey with two pieces of
information: 1) Did they fold their arms with the
left arm on top of right, or with the right arm on top of the left?
2) Did they identify as male or female? The
professor then asked her students to assess whether, in light of
the data from the survey, there was support
for the idea that males and females differed in how often they
folded their arms with their left arm on top of
the right. The survey data indicated that males folded their arms
with their left arms on top more frequently.
But how much more frequently? And was this just a “small-
sample” difference? Or did it accurately reflect a
population-level trend? The data from this experiment are in
armfold.csv. There are two relevant variables:
• LonR_fold: a binary (0/1) indicator, where 1 indicates left arm
on top, and 0 indicates right arm on
top.
• Sex: a categorical variable with levels male and female.
(There’s also a third variable indicating which hand the student

7. writes with, but we’re not using that here.)
Your task (quite similar to what we did with the recidivism R
walkthrough) is to assess support for any
male/female differences in the population-wide rate of “left arm
on top” folding. Make sure to quantify your
uncertainty about how much more often males fold their left
arms on top. (That is, it’s not enough to just
report the estimate for this sample; you have to provide a
confidence interval that tells us how we can expect
this number to generalize to the wider population. In doing so,
you can treat this sample as if it were a
random sample from the relevant population, in this case
university students.) Your write-up should include
four sections:
1) Question: What question are you trying to answer?
2) Approach: What modeling approach did you use to answer
the question?
3) Results: What evidence/results did your modeling approach
provide to answer the question? This
might include numbers, figures, and/or tables as appropriate
depending on your approach.
4) Conclusion: What is your conclusion about your question?
You will want to provide a short written
interpretation of your confidence interval.
Note: for a relatively simple problem like this, each of these
four sections will likely be quite short. Nonetheless,
these sections reflect a good general organization for a data-
science write-up. So we’ll start practicing with
this organization on a simple problem, even if it seems a bit
overkill at first. (It is certainly possibly in this
case for each of them to be only 1 or 2 sentences long. Although

8. you might feel you need more, and although
nobody on our end is breaking out a word counter, it shouldn’t
be too much longer than that.)
Problem 4 - Ebay
In this problem, you’ll analyze data from an experiment run by
EBay in order to assess whether the company’s
paid advertising on Google’s search platform was improving
EBay’s revenue. (It was certainly improving
Google’s revenue!)
Google Ads, also known as Google AdWords, is Google’s
advertising search system, and it’s the primary way
the company made its $162 billion in revenue in fiscal year
2019. The AdWords system has advertisers bid on
certain keywords (e.g., “iPhone” or “toddler shoes”) in order for
their clickable ads to appear at the top of
2
the page in Google’s search results. These links are marked as
an “Ad” by Google, and they’re distinct from
the so-called “organic” search results that appear lower down
the page.
Nobody pays for the organic search results; pages get featured
here if Google’s algorithms determine that
they’re among the most relevant pages for a given search query.
But if a customer clicks on one of the
sponsored “Ad” search results, Google makes money. Suppose,
for example, that EBay bids $0.10 on the
term “vintage dining table” and wins the bid for that term. If a
Google user searches for “vintage dining
table” and ends up clicking on the EBay link from the page of

9. search results, EBay pays Google $0.10 (the
amount of their bid). 1
For a small company, there’s often little choice but to bid on
relevant Google search terms; otherwise their
search results would be buried. But a big site like EBay doesn’t
necessarily have to pay in order for their
search results to show up prominently on Google. They always
have the option of “going organic,” i.e. not
bidding on any search terms and hoping that their links
nonetheless are shown high enough up in the organic
search results to garner a lot of clicks from Google users. So the
question for a business like EBay is, roughly,
the following: does the extra traffic brought to our site from
paid search results—above and beyond what
we’d see if we “went organic”—justify the cost of the ads
themselves?
To try to answer this question, EBay ran an experiment in May
of 2013. For one month, they turned off
paid search in a random subset of 70 of the 210 designated
market areas (DMAs) in the United States. A
designated market area, according to Wikipedia, is “a region
where the population can receive the same or
similar television and radio station offerings, and may also
include other types of media including newspapers
and Internet content.” Google allows advertisers to bid on
search terms at the DMA level, and it infers the
DMA of a visitor on the basis of that visitor’s browser cookies
and IP address. Examples of DMAs include
“New York,” “Miami-Ft. Lauderdale,” and “Beaumont-Port
Arthur.” In the experiment, EBay randomly
assigned each of the 210 DMAs to one of two groups:
• the treatment group, where advertising on Google AdWords
for the whole DMA was paused for a
month, starting on May 22.

10. • the control group, where advertising on Google AdWords
continued as before.
In ebay.csv you have the results of the experiment. The columns
in this data set are:
• DMA: the name of the designated market area, e.g. New York
• rank: the rank of that DMA by population
• tv_homes: the number of homes in that DMA with a
television, as measured by the market research
firm Nielsen (who defined the DMAs in the first place)
• adwords_pause: a 0/1 indicator, where 1 means that DMA was
in the treatment group, and 0 means
that DMA was in the control group.
• rev_before: EBay’s revenue in dollars from that DMA in the
30 days before May 22, before the
experiment started.
• rev_after: EBay’s revenue in dollars from that DMA in the 30
days beginning on May 22, after the
experiment started.
The outcome of interest is the revenue ratio at the DMA level,
i.e. the ratio of revenue after to revenue
before for each DMA. If EBay’s paid search advertising on
Google was driving extra revenue, we would expect
this revenue ratio to be systematically lower in the treatment-
group DMAs versus the control-group DMAs.
On the other hand, if paid search advertising were a waste of
money, then we’d expect the revenue ratio to
be basically equal in the control and treatment groups.

11. 1There’s huge variability in the market price of different search
terms. The market price per click for a search term like
"insurance" or "attorney" or "MBA programs" might be $50 or
more. For stuff you might buy on EBay, it’s usually a lot less.
3
https://en.wikipedia.org/wiki/HTTP_cookie
Two explanatory notes here:
• We use the ratio rather than the absolute difference because
the DMAs differ enormously in population
and therefore revenue.
• We wouldn’t necessarily expect the before-and-after revenue
ratio to be 1 (i.e. similar revenue before and
after the experiment), even in the control-group DMAs. That’s
because, like any retailer, EBay’s sales
exhibit a lot of seasonal patterns and might be lower in some
months across the board, regardless of
paid search. That’s why the important question isn’t whether the
revenue is the same before and after
in the treatment-group DMAs, but whether the before-and-after
ratio is the same for the treatment
group as for the control group.
Your task is compute the average treatment effect and provide a
confidence interval via bootstrapping
to assess the evidence for whether the revenue ratio is the same
in the treatment and control groups, or
whether instead the data favors the idea that paid search
advertising on Google creates extra revenue
for EBay. Make sure you use at least 10000 Monte Carlo
simulations in your bootstrap simulation.

12. Your write-up should include the sections: 1) Question; 2)
Approach; 3) Results; 4) Conclusion as
outlined in Problem 4.
Problem 5 - Creatinine
Download the data in creatinine.csv. Each row represents one of
150 patients from a particular nephrolo-
gist’s office. The variables in this data frame are:
• age: patient’s age in years.
• creatclear: patient’s creatinine clearance rate in mL/minute, a
measure of kidney health (a higher rate
means better clearance, i.e., more healthy).
Use these data to answer three questions:
A) What creatinine clearance rate should we expect for a 36-
year-old? Explain briefly (using one or two
sentences and equations) how you determined this estimate.
B) How does creatinine clearance rate change with age? (This
should be a single number whose units are
ml/minute per year.) Explain briefly (one or two sentences) how
you determined this.
C) Who has a creatinine clearance rate that is healthier (higher)
for their age: a 45-year-old with a rate of
130, or a 60-year-old with a rate of 120? Explain briefly (using
a few sentences and showing your work
with equations) how you determined this.
Problem 6 - Orbital Scanner
If a Resistance ship enters the atmosphere on the desolate rock
planet of Exegol, the probability that the
Imperial fleet’s orbital scanner will correctly register its

13. presence is 95%. If there is, in fact, no Resistance
ship on Exegol, the scanner will falsely register the presence of
a ship with probability 5%. Historical data
indicate that there is a 15% probability at any given time that a
Resistance ship is on Exegol.
Imagine that you are among the Imperial Guard assigned to the
Sith Citadel. Today, the orbital scanner
registers the presence of a Resistance ship. What is the
probability that a Resistance ship is, in fact, on
Exegol? Prepare a short report with this calculation. Don’t
forget to show your work.
Problem 7 - Big Mac Index
From The Economist: "The Big Mac index was invented by The
Economist in 1986 as a lighthearted measure
of the extent to which currencies are at their ‘correct’ level. It
is based on the theory of purchasing-power
parity (PPP), the idea that long-run exchange rates should move
towards the rate that equalises the prices of
an identical basket of goods and services (e.g., a burger) in any
two countries.
4
Burgernomics was never intended as a precise guide of currency
misalignment but rather a tool to make
exchange-rate theory more digestible. Yet the Big Mac index is
now a global standard appearing in economic
textbooks and used in academic studies."
Download bigmac.csv to access a data frame with the following
variables:

14. • date: Date of observation
• iso_a3: Three-character ISO 3166-1 country code
• currency_code: Three-character ISO 4217 currency code
• name: Country name
• local_price: Price of a Big Mac in the local currency
• dollar_ex: Local currency units per dollar
• GDP_dollar: GDP per person, in dollars
Let’s use this dataset to construct and analyze a simpler version
of the Big Mac Index.
Preprocessing
For each observation, create a new variable for the price of a
Big Mac in US Dollars (USD), dividing the
local price by the local currency units per dollar. Before you do
that, however, it’s good practice to account
for any ‘gotchas’ that could happen when dividing—make sure
that the local currency units per dollar are all
positive, non-zero values.
library(tidyverse)
bigmac <- read.csv("bigmac.csv")
bigmac <- bigmac %>% filter(dollar_ex > 0) %>%
mutate(price_usd = local_price/dollar_ex)
For convenience, let’s also add another variable for the year of
the observation date. To do this, use the
function lubridate::year() on the date variable like so:
bigmac <- bigmac %>% mutate(year = lubridate::year(date))
Because each year can possibly have multiple observations per
country, average the USD price across each
country and year to avoid possible duplicates. You should use
the dataset you make here for the subsequent

15. problems. Any references to price refer to the average
calculated in this step.
avg_bigmac <- bigmac %>%
group_by(name, year) %>%
summarise(avg_usd = mean(price_usd, na.rm=TRUE))
Part A: Use boxplots to visualize how the distribution of price
differs by year. Remember the factor()
function for treating numeric variables as categorical.
Based on your plot, what can you say about the price of a Big
Mac over time? In your write-up, include
an informative caption (a few sentences or a short paragraph)
below the plot that identifies the variables
and units plotted on the chart and also summarizes main
takeaways from the plot. Be sure to comment on
measures of both center and spread, as well the presence of
outliers.
Part B: What country had the most expensive Big Mac (in US
Dollars) and how much was it? In what year
was it most expensive?
Part C: Now calculate the actual big mac index for 2021. This is
the percentage difference of the price of a
Big Mac in a given locale relative to the price of a Big Mac in
the United States. I stored my US Big Mac
price in a variable for easy reference later (the pull() command
returns just numbers, no fancy dataframe
stuff):
us_price <- avg_bigmac %>% filter(year==2021,
name=="United States") %>% pull(avg_usd)
Take the top 20 values of the index and plot them, sorted

16. ascending or descending. Useful functions here are
top_n or slice_max() (see documentation for examples of
usage). You may also want to use reorder()
where you can pass to your axis aesthetic the label and var iable
to sort on. For example, if I wanted the
5
country as one of my plot variables, I could use
reorder(country, big_mac_index) in place of just country
to sort them by the values of my Big Mac index variable. If you
are having trouble with slice_max() try
piping your dataframe to ungroup() then piping it to
slice_max().
Part D: Address the following questions with a few sentences
(no more than a short paragraph) in your
write-up: - Which country’s currency is most overvalued
relative to the United States? By how much? - Are
there more overvalued or undervalued currencies, relative to the
US? - What problems might you foresee
with the index as we’ve currently calculated it?
6
Homework 2Problem 1 - NHANESProblem 2 - Iron
BankProblem 3 - ArmfoldProblem 4 - EbayProblem 5 -
CreatinineProblem 6 - Orbital ScannerProblem 7 - Big Mac
IndexPreprocessing