2nd
Hourly
Math 1107
You will use only the following
resources:
Your
individual calculator;
Your
individual tool-sheet (one (1) 8.5 by 11 inch sheet);
Your writing
utensils;
Blank
Paper (provided by me);
Do not share these resources with anyone else.
Show
complete detail and work for full credit.
Follow case study solutions and sample hourly keys in
presenting your solutions.
Work all four cases.
Using
only one side of the blank sheets provided, present your work. Do not write on
both sides of the sheets provided, and present your work only on these sheets.
Do not share information with
any other students during this hourly.
When you are finished:
Prepare a Cover Sheet: Print
your name on an otherwise blank sheet of paper. Then stack your stuff as
follows:
Cover Sheet (Top)
The Test Papers
Your Toolsheet
Then hand all of this in to me.
Sign and Acknowledge: I agree to follow
this protocol.
________________________________________________________________________
Descriptive
Statistics
A company, BarrelCorpÔ manufactures barrels and wishes to ensure the strength and quality of its barrels. Chimpanzees traumatized the company owner as a youth; so the company uses the following test (Angry_Barrel_of_Monkeys_Test) of its barrels:
Ten (10) chimpanzees are loaded into the barrel. The chimpanzees are exposed to Angry!Monkey!Gas!ä,
an agent guaranteed to drive the chimpanzees to a psychotic rage. The angry,
raging, psychotic chimpanzees then destroy the barrel from the inside in an
angry, raging, psychotic fashion. The survival time, in minutes, of the barrel
is noted.
A random sample of 30 BarrelCorpÔ barrels is evaluated using the Angry_Barrel_of_Monkeys_Test, and the survival time in minutes of each barrel is noted. The survival time of each barrel is listed below:
.50, .75, 1, 1, 2, 3, 4, 5, 7, 7, 7.5, 8, 8.3, 8.5, 9, 9.5, 9.75, 10, 12, 12, 14, 23, 25, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 34, 34, 35, 36, 37, 38, 39, 40, 41, 42, 51, 53, 54, 56, 57, 58, 62, 65, 70, 75, 77, 80, 85, 90, 240
Compute and interpret the
following statistics: sample size, p00, p25, p50, p75, p100, (p100-p75),
(p75-p25), (p50-p25).
Serum
Creatinine and Kidney (Renal) Function
Healthy kidneys remove wastes and excess fluid from the blood. Blood tests show whether the kidneys are failing to remove wastes. Urine tests can show how quickly body wastes are being removed and whether the kidneys are also leaking abnormal amounts of protein. The nephron is the basic structure in the kidney that produces urine. In a healthy kidney there may be as many as 1,000,000 nephrons. Loss of nephrons reduces the ability of the kidney to function by reducing the kidney’s ability to produce urine. Progressive loss of nephrons leads to kidney failure.
Serum creatinine. Creatinine is a waste product that comes from meat protein in the diet and also comes from the normal wear and tear on muscles of the body. Creatinine is produced at a continuous rate and is excreted only through the kidneys. When renal dysfunction occurs, the kidneys are impaired in their ability to excrete creatinine and the serum creatinine rises. As kidney disease progresses, the level of creatinine in the blood increases.
Table: Serum Creatinine and Kidney
Function
|
Serum Creatinine (mg/dL)* |
Approximate Nephron Loss |
Comments |
|
[.6,1.5] |
Less than 50% of nephrons lost |
Normal Function |
|
(1.5,4.8) |
Between 50% and 75% of nephrons
lost |
Problem |
|
[4.8,10] |
Between 75% and 90% of nephrons
lost |
Bigger Problem |
|
(10,+) |
More than 90% of nephrons lost |
End Stage Renal Disease |
*: milligrams of creatinine per
deciliter of serum
Suppose that we sample serum
creatinine levels in a random sample of adults. Serum creatinine (as mg/dL) for
each sampled subject follows:
15.0, 13.8, 13.5, 13.1, 12.1, 11.1, 10.0, 9.8, 8.1, 7.3, 5.1, 5.0, 4.9,
4.8, 4.0, 3.5, 3.3, 3.2, 3.2, 2.9, 2.5, 2.3, 2.0, 2.0, 1.9, 1.9, 1.7, 1.6, 1.5,
1.5, 1.4, 1.4, 1.3, 1.3, 1.2, 1.2, 1.2, 1.1, 1.1, 1.0, 1.0, 0.9, 0.9, 0.9, 0.8,
0.8, 0.8, 0.7, 0.6, 0.6
Let m denote the sample mean, and sd the sample standard
deviation. Compute and interpret the intervals m ± 2sd and m ± 3sd,
using Tchebysheff’s Inequalities and the Empirical Rule. Be
specific and complete. Show your work, and discuss completely for full credit.
Case
Three
Coronary Artery Disease
The
heart continuously pumps blood enriched with oxygen and vital nutrients through
a network of arteries to all parts of the body's tissues. The heart muscle
itself needs a plentiful supply of oxygen-rich blood, which is provided through
a network of coronary arteries. These arteries carry oxygen-rich blood to the
heart's muscular walls (the myocardium). Coronary Artery Disease is the
most common cause of heart attacks, which occurs when blood flow to the
myocardium is interrupted. Heart attack occurs when blood flow is blocked and
tissue death occurs from loss of oxygen, severely damaging the heart. Coronary
artery disease is the end result of a complex process commonly called
"hardening of the arteries"). This causes blockage of arteries and
prevents oxygen-rich blood from reaching the heart.
Angioplasty and Stents
A cardiovascular stent props open clogged heart arteries. During an angioplasty, cardiologists use a balloon to push aside heart disease-causing clogs. The opening created by the action of the inflated balloon frequently re-clogs without further intervention. The use of stents is one form of intervention. Stents, a type of metal scaffolding, may be inserted to help keep the artery from re-clogging. Complications from cardiovascular stents can stem from inflammation, clotting and bleeding due to interactions between the stent (usually metallic), the vascular tissue and blood cells. Medicated stents may reduce some of these complications. One accepted approach is to coat stents with drugs that inhibit blood clotting, for example, heparin coated stents are currently FDA licensed. Another approach involves treating the inflammation near the stent site. If the inflammation can be managed, it is thought that clot formation may be reduced. Consider an anti-inflammatory coated stent. Sirolimus is one such drug. A sirolimus coated stent may help control inflammation, thus fighting a new clog, when the artery slowly absorbs some of the drug.
Sketch a comparative clinical
trial for Heparin Coated Stents versus Sirolimus Coated Stents in
the treatment of patients with Coronary Artery Disease. Make your sketch
concise and complete, following the style demonstrated in class, in the second
hourly and in case study summaries.
Design Fault Spot
In each of the following a brief description of a design is presented. Briefly identify faults present in the design. Use the information provided. Be brief and complete.
4.a): WidgetCorpsÔ is conducting an Employee Satisfaction Survey. They hire a third
party to conduct the survey, and a
random sample of employees is employed in the survey. The interviews are
conducted after the annual performance and salary reviews, and while the third party
identifies the identities of the respondents on the surveys, it tells the
respondents that these will be removed before the results are given to
WidgetCorpsÔ.
4.b): A sample survey design employs a random sample
of United Kingdom (England, Wales, Scotland, and Northern Ireland) adult
subjects (18 years or older, non-institutionalized). The research objective of
the survey is to determine attitudes of Irish subjects regarding Birth Control.
Assume that the Survey Instrument is written properly and delivered in an
unbiased way.
4.c): A clinical trial of a new Hepatitis C treatment is designed as follows: subjects are screened for Hepatitis C infection. Those who test positive for Hepatitis C infection are then told of their status, and are offered “free treatment” for Hepatitis C at no cost, and are given no further information. Those who accept the free treatment offer are then randomly assigned to either a Placebo, or to the New Treatment Plan.
4.d): The objective of a sample survey is to
study the attitudes of urban residents of the United States regarding federal
programs, taxation and spending. A random sample of urban business owners is
employed in this design. Assume that there are no problems with the wording and
delivery of the survey instrument.