Alliant International University

Research II: Data Analysis & Advanced Statistics

Due Date:

Saturday, Feb. 15, 2003

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.

• (HW_2_1) Using the following data for the Mean Absorbance Ration (MAR) scores from the ELISA HIV antibody test answer the following questions (assume the prevalence of HIV in the US is 1%):
 MAR Healthy Donor HIV < 2 202 0 2.0 - 2.99 73 2 _(test threshold)_ 3.0 - 3.99 3 7 4.0 - 4.99 15 7 5.0 - 5.99 2 15 6.0 - 11.99 2 36 > 12.0 0 21 Total: 297 88
• Identify the false-positive (Type I) and false-negative (Type II) errors. What is the power of the test?
• P(Negative Test | Not-HIV)=?  P(HIV & Positive Test)=?
• How do we choose the best threshold-value for a test like that?
• Suppose a choose a random subject from the pool of individuals that participated in this study. What is the probability that the subject is:
• positive on the MAR test?
• of Hispanic race?
• either HIV-positive & has negative test, or Non-HIV and has positive test?

• (HW_2_2) The Los Angeles Mayor is interested in assessing the population satisfaction with the performance of the Police Department (PD) and the District Attorney (DA) office in one county. You are contracted to do the study and report to the Mayor.
• Who should you poll? Do you attempt a cencus or do a well-designed controlled poll/survey?
• What sample size(s) would you use? What criteria you need to satisfy to argue about the validity of your final conclusions?
• How to collect the survey responses? Do you ask the same people if they are satisfied (S) or dissatisfied (D) with the LAPD and separetely the LADA office?
• Suppose you split your pool of participants into two groups, each expressing their opinion on the PD or DA work. Let your sample sizes be nPD=1,000 and nDA=1,2000 and proportion of satisfied citizens be pPD=0.6 and pDA=0.7, respectively. The Mayor wants to commit more resources to the law enforcement agency that  does the best job, and replace the Head of the other agency that has not done well in the publics eyes. How to evaluate if there is evidence for statistical differences between these satisfaction rates?
• How do you communicate your results to the Mayor's office, to avoid misinterpretation of your analysis.

• (HW_2_3) Suppose the probability of acquital (A) given DNA match (M) is 0.245. What is the probability that someone has a DNA matching the sample taken at the crime scene, given that the subject was convicted (Ac)? Assume a DNA match could occur randomly only with probability of 0.001 of population and P(conviction | No DNA match) = 0.1.