Key|The 2^nd Hourly | Math 1107 | Fall Semester 2010

Protocol

You will use only the following resources: Your individual calculator; individual tool-sheet (one (1) 8.5 by 11 inch sheet), writing utensils, blank paper (provided by me) and this copy of the hourly.

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. Write on one side only 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), Your Work Sheets, The Test Papers, Your Toolsheet. Then hand all of this in to me.

Sign and Acknowledge: I agree to follow this protocol.

Name (PRINTED) Signature Date

Case One | Descriptive Statistics | Credit Scores

Fair Isaac Corporation developed a consumer credit score, a number that summarizes the risk present in lending money to a consumer. The consumer credit score ranges from 300 to 850. Credit bureau scores are often called “FICO scores” because most credit bureau scores used in the U.S. are produced from software developed by Fair Isaac and Company. FICO scores are provided to lenders by the major credit reporting agencies. Suppose that credit scores are observed for a random sample of US residents taken in July of 2007:

350, 375, 450, 535, 576, 585, 590, 625, 640, 661, 669, 670, 673, 675, 679, 680, 685, 688, 691, 695, 700, 701 705, 706, 707, 713, 723, 727, 740, 743, 752, 755, 757, 759, 761, 774, 774, 775, 783, 785, 791, 794, 798, 801 805, 810, 815, 827, 830, 845

Compute and interpret the following statistics: sample size, p00, p25, p50, p75, p100, (p100 – p25),

(p75 – p25), (p50 – p25).

n=50 | There are 50 US residents in our sample, each contributing a July 2007 FICO score.

p₀ = 350 | The lowest credit score in the sample was 350.

p₂₅ = 673 | Approximately 25% of the credit scores in the sample were at 673 or lower.

p₅₀ = 710 | Approximately 50% of the credit scores in the sample were at 710 or lower.

p₇₅ = 775 | Approximately 75% of the credit scores in the sample were at 775 or lower.

p₁₀₀ = 845 | The highest credit score in the sample was 845.

range₄₁ = p₁₀₀ – p₂₅ = 845 – 673 = 172 | Approximately 75% of the scores in the sample were between 673 and 845. The largest possible difference in credit score between any pair of residents in the upper ¾ sample is 172.

range₃₁ = p₇₅ – p₂₅ = 775 – 673 = 102 | Approximately 50% of the scores in the sample were between 673 and 775. The largest possible difference in credit score between any pair of residents in the middle half sample is 102.

range₂₁ = p₅₀ – p₂₅ = 710 – 673 = 37 | Approximately 25% of the scores in the sample were between 673 and 710. The largest possible difference in credit score between any pair of residents in the lower quarter sample is 37.

Case Two | Summary Intervals | Credit Scores

Using the data and context of Case One, Let m denote the sample mean spot count, 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.

lower2 = m – (2*sd) ≈ 702.96 – (2*106.19) ≈ 489.16 [489]

upper2 = m + (2*sd) ≈ 702.96 + (2*106.19) ≈ 916.76 [850]

lower3 = m – (3*sd) ≈ 702.96 – (3*106.19) ≈ 382.26 [383]

upper3 = m + (3*sd) ≈ 702.96 + (3*106.19) ≈ 1023.66 [850]

There are 50 FICO credit scores in the sample, each drawn from a US resident during July of 2007.

At least 75% of the credit scores in the sample are between 489 and 850.

At least 89% of the credit scores in the sample are between 383 and 850.

If the FICO scores for US residents for July 2007 cluster symmetrically around a central value, becoming rare as distance from the center increases, then:

approximately 95% of the credit scores in the sample are between 489 and 850 and approximately 100% of the credit scores in the sample are between 383 and 850.

Case Three | 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.

3.1) The objective of a sample survey is to study the attitudes of urban business owners of the United States regarding federal programs, taxation and spending. A random sample of urban residents is employed in this design. Assume that there are no problems with the wording and delivery of the survey instrument.

The survey must sample the appropriate target population – owners of urban businesses. Not every urban resident owns an urban business, and not urban business owner resides in the city.

3.2) In a comparative clinical trial, treatment methods are compared in the treatment of Condition X, which when left untreated leads to severe complications and possibly death. A new surgical method is compared to a standard surgical method. Study physicians classify subjects by the severity of their disease, and assign only the "moderate" subjects to the new surgical method. Only the "severe" subjects are assigned to the standard surgical method.

Randomly assign subjects to treatment without regard to disease severity.

3.3) A random sample of parents of college/university first-year undergraduate students is surveyed about the study practices of their children. The survey questionnaire was properly written, and the sample of parents randomly and reasonably selected. The parents responded to questions about their children's study habits.

The survey must sample the appropriate target population – first-year undergraduates. The parents need not be a reliable source of information regarding their children’s study habits.

3.4) In a proposed clinical trial, treatment methods are compared in the treatment of Condition Z, which when left untreated leads to severe complications and possibly death. Suppose we have a new candidate treatment, and further suppose that a standard treatment for a similar (but different) disease is available. A comparative clinical trial is proposed that would compare these treatments in patients with condition Z.

Use of the standard treatment(for a different condition) is inappropriate for this trial, unless that treatment also serves as a standard treatment for CZ, or if it is being considered an experimental treatment for CZ. If a standard treatment for CZ is available, use it – otherwise, use a placebo group as a basis for comparison.

Case Four | Clinical Trial Sketch | Crohn's Disease

Crohn's disease is a chronic inflammation of the intestinal wall. Most often, lower areas of the small intestine (ileum) are involved, although any part of the digestive tract (from the mouth to the anus) may be involved. Symptoms of Crohn's disease include: chronic diarrhea, crampy abdominal pain, fever, suppressed appetite and weight loss. Complications of Crohn's disease include: intestinal obstructions, abnormal connections within the intestines, abnormal connections of the intestines and bladder, abnormal connections of the intestines and the skin surface, and intestinal infections. In children, symptoms may include joint inflammation, slow growth, fever and anemia. Treatments of Crohn's disease depend on the symptoms being treated. For infections, broad spectrum anti-biotics are employed. For inflammation, cortico-steriods are used, as well as other anti-inflammatories. Additionally, certain medications focus on the immune system for general symptom reduction, as well as keeping Crohn's disease in remission. Cortico-steroids are used to provide relief for inflamed areas of the body. They lessen swelling, redness, itching, and allergic reactions.

A standard treatment of Crohn’s disease is mesalamine, a drug that reduces inflammation in the large intestine (colon). Budesonide is an orally administered, non-systemic cortico-steroid that is released in the intestine, where it works locally and topically to decrease inflammation. Budenoside is metabolized in a way that minimizes side effects. Hopefully, patients taking budesonide experience fewer of the typical side effects associated with other cortico-steroids used to treat Crohn's Disease, such as prednisone or prednisolone tablets, because most of budesonide is not absorbed into the body.

Possible side effects of cortico-steroids include: lowered resistance to infections, persistent infections, decreased or blurred vision; frequent urination; increased thirst, abdominal or stomach pain or burning, headache; irregular heartbeat; menstrual problems; muscle cramps or pain; muscle weakness; nausea.

Sketch a comparative clinical trial for budesonide versus mesalamine in the treatment of large intestinal (colon) inflammation in patients with Crohn's disease. Make your sketch concise and complete, following the style demonstrated in class, in the sample second hourlies and in case study summaries.

A Comparison of Budesonide and Mesalamine for Active Crohn's Disease (N Engl J Med 1998:339;370 - 374)

We recruit subjects with Chrohn’s disease affecting the large intestine/colon. Those giving informed consent and who meet appropriate inclusion and exclusion criteria are enrolled in the trial.

Enrolled subjects are randomly assigned to either Budesonide with Placebo_Mesalamine or to Placebo_Budesonide + Mesalamine. Double-blinding is employed, so that neither the subjects nor the clinical workers know individual treatment status.

Treated subjects are followed for toxicity(organ damage, especially kidney/liver),

side effects (including lowered resistance to infections, persistent infections, decreased or blurred vision; frequent urination; increased thirst, abdominal or stomach pain or burning, headache; irregular heartbeat; menstrual problems; muscle cramps or pain; muscle weakness; nausea) and

effectiveness (including chronic diarrhea, crampy abdominal pain, fever, suppressed appetite and weight loss. Complications of Crohn's disease include: intestinal obstructions, abnormal connections within the intestines, abnormal connections of the intestines and bladder, abnormal connections of the intestines and the skin surface, and intestinal infections. In children, symptoms may include joint inflammation, slow growth, fever and anemia). Quality of life may also be considered.

Work all four (4) cases.