Key

The 2nd Hourly

Math 1107

Fall Semester 2009

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 | Fictitious Striped Lizard

 

 

 

The Fictitious Striped Lizard (FSL) is a native species of Lizard Island, and is noteworthy for the both the quantity and quality of its stripes. Consider a random sample of FSL, in which the number of stripes per lizard is noted:

 

 

 

29, 17, 13, 18, 21, 11, 12, 22, 10, 17, 18, 22, 22, 20, 19, 14, 18, 17, 8, 9, 17, 15, 5, 6, 10, 8, 11, 17, 15, 8,

14, 5, 6, 9, 16, 13, 6, 20, 20, 14, 5, 20, 7, 21, 17, 12, 14, 16, 12, 13, 16, 14, 10, 12, 14, 13, 15, 5, 1, 4, 13

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

n        p00        p25      p50      p75     p100    range41    range31    range30

61       1          10       14       17       29       19         7          16

 

range41 = p100 - p25 = 29 - 10 = 19

range31 = p75 - p25 = 17 - 10 = 7

range30 = p75 - p00 = 17 - 1 = 16

 

There are 61 Fictitious Striped Lizards in the sample.

The lizard in the sample with the fewest stripes has one stripe.

Approximately 25% of the lizards in the sample have 10 or fewer stripes.

Approximately 50% of the lizards in the sample have 14 or fewer stripes.

Approximately 75% of the lizards in the sample have 17 or fewer stripes.

The lizard in the sample with the most stripes has 29 stripes.

 

Approximately 75% of the lizards in sample have between 10 and 29 stripes. The largest difference in stripe count between any pair of lizards in this upper ¾ sample is 19 stripes.

 

Approximately 50% of the lizards in sample have between 10 and 17 stripes. The largest difference in stripe count between any pair of lizards in this middle half  sample is 7 stripes.

 

Approximately 75% of the lizards in sample have between 1 and 17 stripes. The largest difference in stripe count between any pair of lizards in this lower ¾ sample is 16 stripes.

 

Case Two | Summary Intervals | Fictitious City Half Marathon

 

A half marathon is an event in which runners complete a course of approximately 13.1 miles. Suppose that we have a random sample of finishers of the 2008 Fictitious City Half Marathon, whose finishing times (in hours) are listed below:

 

1.03, 1.04, 1.08, 1.10, 1.22, 1.25, 1.30, 1.35, 1.40, 1.45, 1.50, 1.55, 1.60, 1.72, 1.75, 1.77, 1.80, 1.83, 1.85, 1.89, 1.90, 1.95, 2.00, 2.25, 2.30, 2.33, 2.40, 2.45, 2.50, 2.55, 2.57, 2.60, 2.63, 2.65, 2.70, 2.75, 2.78, 2.90, 2.95, 3.20, 3.22, 3.25, 3.27, 3.30, 3.35, 3.37, 3.39, 3.40, 3.45, 3.52, 3.62, 3.75, 3.90, 4.00, 4.08, 4.13

 

Let m denote the sample mean finish time, 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.

 

n       m          sd      lower2sd    upper2sd    lower3sd    upper3sd

56    2.44357    0.89627     0.65104     4.23611    -0.24523     5.13238

 

lower2sd = m – 2*sd = 2.44357 - 2*0.89627 = 0.65104

upper2sd = m + 2*sd = 2.44357 + 2*0.89627 = 4.23611

lower3sd = m – 3*sd = 2.44357 - 3*0.89627 = -0.24523[0]

upper2sd = m + 3*sd = 2.44357 + 3*0.89627 = 5.13238

 

At least 75% of the 2008 Fictitious City Half Marathon runners in the sample finished in between .65 and 4.2 hours.

At least 89% of the 2008 Fictitious City Half Marathon runners in the sample finished in between 0 and 5.1 hours.

 

If  the finishing times for the 2008 Fictitious City Half Marathon finish times cluster symmetrically around a central value, becoming rare as the distance from the center increases, then:

 

Approximately 95% of the 2008 Fictitious City Half Marathon runners in the sample finished in between .65 and 4.2 hours.

Approximately 100% of the 2008 Fictitious City Half Marathon runners in the sample finished in between 0 and 5.1 hours.

 

 

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 clinical trial of a new Hepatitis C (HepC) treatment is designed as follows: subjects are screened for HepC   

infection. Untreated HepC can lead to liver disease, liver failure, liver cancer and death. Those who test positive for HepC infection are then told of their status, and are offered treatment for HepC at no cost, and are offered enrollment in a comparative clinical trial for the treatment of HepC infection. Those who qualify and who give informed consent are then stratified by risk of progression to symptoms of hepatitis. Those judged to be at high risk are assigned to the new treatment, those judged to be at moderate risk of progression to symptoms of hepatitis are assigned to standard treatment, and those judged to be at minimal risk of progression to symptoms of hepatitis symptoms are assigned to placebo only.

Lack of informed consent, inappropriate use of placebo, inappropriate denial of treatment, non-random assignment to treatment.

2. A sample survey of US University and College undergraduates is used to study the sexual habits, knowledge and attitudes of their parents and legal guardians. Appropriate random sampling of students is used, and there are no problems with the wording and delivery of the survey instrument.

Inappropriate use of proxy respondents – ask the parents directly.

3. WidgetCorpsä 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 WidgetCorpsä.

 

Identification of the respondents may affect confidentiality. If the survey is given too soon after reviews, responses may be distorted.

 

4. Disease W is a disease caused by an infection. Left untreated, disease W produces severe and occasionally fatal symptoms and complications. Suppose that no effective, standard treatments are available. Suppose further that a new treatment, ugorbitx is available for evaluation. A clinical trial is proposed to evaluate ugorbitx by giving all trial subjects ugorbitx. Their results would be compared to similar groups of untreated patients who are not enrolled in the trial.

 

Inappropriate comparison – use an internal control group by randomly assigning subjects to either treatment or placebo.

 

Case Four | Clinical Trial Sketch | 2009 H1N1 Vaccine Trial

 

Image of H1N1 influenza virus

This is a new influenza A(H1N1) virus that has never before circulated among humans. This virus is not related to previous or current human seasonal influenza viruses.

Signs of influenza A(H1N1) including fever, cough, headache, muscle and joint pain, sore throat and runny nose, and sometimes vomiting and diarrhea.

Influenza is a disease characterized by fever, cough, headache, muscle and joint pain, sore throat, congestion, and occasionally nausea and diarrhea. It is caused by a family of viruses, all of which mutate from year to year. The 2009 H1N1 influenza virus is a type A strain that is distinct from previous influenza viruses. It is distinct in that it is more easily transmitted than the usual strains of influenza viruses and in that it causes serious complications in subpopulations not usually endangered by the usual strains of influenza viruses. Serious complications of influenza include pneumonia and respiratory failure.

 

 

A vaccine reduces or prevents infection by exposing a person’s immune system to selected components of a virus – this exposure leads to the production of antibodies specifically designed to attack the original virus. An effective vaccine induces the production of relevant antibodies, and these antibodies then enhance the ability of a vaccinated person to resist infection by the original virus.

 

 

 

Case Four | Clinical Trial Sketch | 2009 H1N1 Vaccine Trial

 

The 2009 H1N1 Influenza virus is sufficiently distinct from other strains of influenza viruses that a new vaccine is needed. Suppose that we have developed a new vaccine, H1N12009NXVax, based on a live, but attenuated (weakened) H1N1 influenza virus. 

 

Inclusion Criteria: are males or non-pregnant females age 18 and older, are in good health, are not infected with influenza, are able to understand and comply with planned study procedures and can provide written informed consent prior to initiation of any study procedures.

 

Exclusion Criteria: have a known allergy to eggs or other components of the vaccine, are pregnant, have suppressed immune system, have cancer, use steroids or any immuno-suppressive drugs, have been recently vaccinated, have a prior history of severe reactions following previous immunization with influenza virus vaccines, had a recent fever, had a prior H1N1 vaccine or infection within the past two years.

 

Outcome Measures: Safety: Occurrence of vaccine-associated serious adverse events, including severe allergic reactions to the vaccine. Immune: Achieving a significant immune response, measured as an increase in H1N1 specific antibodies. Prevention: Lower incidence of H1N1 influenza among vaccinated subjects.

Sketch a basic clinical trial evaluating the safety and effectiveness of the new vaccine in the production of relevant antibodies and in the prevention of H1N1 influenza. Make your sketch concise and complete, following the style demonstrated in class, in the sample second hourlies and in case study summaries.

We recruit H1N1-free males or non-pregnant females age 18 and older, are in good health, are not infected with influenza, are able to understand and comply with planned study procedures and can provide written informed consent prior to initiation of any study procedures. Those who meet all inclusion/exclussion requirements, and who give informed consent are enrolled in the trial.

 

Study subjects are randomly assigned to either  H1N12009NXVax or to a placebo version of H1N12009NXVax. Double blinding is employed, so that neither the subjects nor the study personnel know the actual treatment assignments.

 

Treated subjects are then tracked for occurrence of vaccine-associated serious adverse events, including severe allergic reactions to the vaccine, significant immune response, measured as an increase in H1N1 specific antibodies and for incidence of H1N1 influenza, as well as other side effects and toxicity.

 

 

Work all four (4) cases.