Key | The 2^nd Hourly | Math 1107 | Spring Semester 2011

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 | Angry Barrels of Monkeys

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) Ô 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 BarrelCorpÔ barrels is evaluated using the Angry_Barrel_of_Monkeys_TestÔ, and the survival time in minutes of each barrel is noted. The survival time of each barrel is listed below:

.75, .75, .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, 31, 31, 32, 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, 105

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

Numbers

n p00 p25 p50 p75 p100 R41 R31 R30

62 0.75 9 31 42 105 96 33 41.25

range₄₁ = p₁₀₀ – p₂₅ = 105 – 9 = 96

range₃₁ = p₇₅ – p₂₅ = 42 – 9 = 32

range₃₀ = p₇₅ – p₀₀ = 42 – 0.75 = 41.25

Interpretation

There are 62 BarrelCorpÔ barrels in our sample.

The BarrelCorpÔ barrel in our sample with the shortest survival time survived .75 minutes (45 seconds) of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 25% of the BarrelCorpÔ barrels in our sample survived 9 minutes or less of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 50% of the BarrelCorpÔ barrels in our sample survived 31 minutes or less of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 75% of the BarrelCorpÔ barrels in our sample survived 42 minutes or less of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

The BarrelCorpÔ barrel in our sample with the longest survival time survived 105 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 75% of the BarrelCorpÔ barrels in our sample survived between 9 and 105 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure. The largest possible difference in survival time between any pair of barrels in our upper-three-quarter sample is 96 minutes.

Approximately 50% of the BarrelCorpÔ barrels in our sample survived between 9 and 42 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure. The largest possible difference in survival time between any pair of barrels in our middle half sample is 32 minutes.

Approximately 75% of the BarrelCorpÔ barrels in our sample survived between .75 and 42 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure. The largest possible difference in survival time between any pair of barrels in our lower-three-quarter sample is 41.25 minutes.

Case Two | Summary Intervals | Pick’s Disease

Pick's disease (Frontotemporal Dementia) is a relatively rare, degenerative brain illness that causes dementia. The first description of the disease was published in 1892 by Arnold Pick. Pick's disease is marked by "Pick bodies", rounded, microscopic structures found within affected cells. Neurons swell, taking on a "ballooned" appearance. Pick's disease is usually sharply confined to the front parts of the brain, particularly the frontal and anterior temporal lobes. The first symptoms of Pick's disease are often personality change, and a decline in function at work and home. Eventually, they enter a terminal vegetative state. Suppose that we identify a random sample of deceased cases of Pick’s Disease – time from initial diagnosis to death is given in years:

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 ,6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 13.

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.

Numbers

lower2 = m – (2*sd) ≈ 5.71014 – (2*2.73378) ≈ 0.24258 [Approximately 3 months after Dx]

upper2 = m + (2*sd) ≈ 5.71014 + (2*2.73378) ≈ 11.1777

lower3 = m – (3*sd) ≈ 5.71014 – (3*2.73378) ≈ -2.49121[0/Within first year after Dx]

upper3 = m + (3*sd) ≈ 5.71014 + (3*2.73378) ≈ 13.9115

Interpretation

At least 75% of the Pick’s disease patients in our sample survived between 3 months and 11.1 years after diagnosis.

At least 89% of the Pick’s disease patients in our sample survived 13.9 years or less after diagnosis.

If the survival times for Pick’s disease patients cluster symmetrically around a central value, becoming rare as distance from the center increases, then approximately 95% of the Pick’s disease patients in our sample survived between 3 months and 11.1 years after diagnosis and approximately 100% of the Pick’s disease patients in our sample survived 13.9 years or less after diagnosis.

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.

1. A sample of college students is needed for a sample survey. The people running the study decide on the

following: they divide the population of colleges and universities into groups based upon enrollment size and whether the college or university is private or public; next, they used judgment to select one school from each group. Then, a random sample of students was selected from each selected school.

The first stage of sampling is not random – select the schools randomly in the first stage, then randomly sample students within each selected school.

2. In a comparative 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.

If no standard of care for Z exists, the basis for comparison is placebo. If a standard of care for Z exists, then that standard treatment is the basis for comparison – the “standard” treatment is not presented as standard treatment for Z.

3. 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.

Assign treatments in a random fashion.

4. Sample survey planning is under way to study voter support levels for a proposed (federal) constitutional amendment. The proposal is to randomly sample US resident adults, aged 18 years or older.

Randomly sample registered voters.

Case Four | Clinical Trial Sketch | Tamoxifen and Raloxifene for the Prevention of Breast Cancer

The purpose of this study is to examine the performance of the drug Raloxifene (relative to the drug Tamoxifen) in reducing the incidence of breast cancer in postmenopausal women₁ who are at increased risk of the disease₂.

1. Postmenopausal women at increased risk for developing invasive breast cancer, who meet one of the following criteria: At least 12 months since spontaneous menstrual bleeding; Prior documented hysterectomy and the surgical removal of fallopian tubes and ovaries; At least 55 years of age with prior hysterectomy with or without surgical removal of the ovaries; Aged 35 to 54 years with a prior hysterectomy without surgical removal of the ovaries or with a status of ovaries unknown with documented follicle-stimulating hormone level demonstrating elevation in postmenopausal range. 2. Women without prior breast cancer, but who are at elevated risk for breast cancer: Histologically confirmed lobular carcinoma in situ treated by local excision only or at least 1.66% probability of invasive breast cancer within 5 years using Breast Cancer Risk Assessment Profile; No clinical evidence of malignancy on physical exam within the past 180 days; No evidence of suspicious or malignant disease on bilateral mammogram within the past year; No bilateral or unilateral prophylactic mastectomy and No prior invasive breast cancer or intraductal carcinoma in situ

Objectives: Determine whether Raloxifene is more or less effective than Tamoxifen in significantly reducing the incidence rate of invasive breast cancer in postmenopausal women; Evaluate the effects of Tamoxifen and Raloxifene on the incidence of intraductal carcinoma in situ, lobular carcinoma in situ, endometrial cancer, ischemic heart disease, fractures of the hip and spine, or Colles' fractures of the wrist in these participants; Evaluate the toxic effects of these regimens in these participants and Determine the effect of these regimens on the quality of life of these participants.

Sketch a comparative clinical trial to evaluate the drug Raloxifene (relative to the drug Tamoxifen) in reducing the incidence of breast cancer in postmenopausal women₁ who are at increased risk of the disease₂. Make your sketch concise and complete, following the style demonstrated in class, in the second hourly and in case study summaries.

We recruit women who are postmenopausal and who are at increased risk for developing invasive breast cancer, and who are without prior breast cancer, but who are at elevated risk for breast cancer. After briefing our volunteers on the details, risks and possible benefits of participation, those volunteers who qualify and who give informed consent are enrolled in the trial.

We randomly assign enrolled subjects to either Raloxifine with Placebo_Tamoxifen or to Tamoxifen with Placebo_Raloxifene, employing double-blinding, so that neither the subjects nor their clinical staff know the individual treatment status of any study subject during the study.

Treated subjects are followed for drug safety issues, including kidney, liver and other major organ-related problems or toxicity. Treated subjects are followed for the emergence of breast cancer and time-to-cancer in those who present breast cancer. In full detail, treated subjects are followed for invasive breast cancer, intraductal carcinoma in situ, lobular carcinoma in situ, endometrial cancer, ischemic heart disease, fractures of the hip and spine, or Colles' fractures of the wrist.

Work all four (4) cases.