Question 1:
For each of the statements below choose ONE of the following four options, AND ALSO explain your rationale:
- Necessary and sufficient
- Necessary but not sufficient
- Not necessary but sufficient
- Not necessary and not sufficient
(Note: You are to assume the statements below are correct, even if you think/know they are not)
1- Hepatitis B virus is present in all Hepatitis B patients. However, some of the infected will never develop Hepatitis B and remain as silent carriers
2- Helicobacter pylori are identified in many gastric ulcer patients. Most people who test positive for H pylori have or will develop gastric ulcer
3- The unavoidable impact of collision of a fast-moving, heavy blunt object to the skull is brain hemorrhage
4- All AIDS patients are HIV positive. All individuals who have HIV will eventually develop AIDS

Question 2:
In 1993 a case control study was conducted to assess a possible association between serving in the Persian Gulf War in 1991 and the subsequent diagnosis of neurological diseases. Researchers compared the military records of 750 Army soldiers seen for neurological symptoms to 1500 Army soldiers seen for non-neurological symptoms. In late 1991 and 1992 Army officials were concerned about the health of soldiers who served in the Persian Gulf War. They were therefore more likely to refer soldiers with neurologic symptoms who had served in the Persian Gulf War vs. Army soldiers with similar symptoms who had not served in the Persian Gulf War. The study concluded that Army soldiers who served in the Persian Gulf War had 50% more risk of having subsequent neurological disease vs. those who did not serve in the Gulf War.
a- Do you think this conclusion is correct? Discuss your analysis and rationale.
Subsequent analyses showed that the investigators often failed to identify subjects with mild neurological diseases among those who did not serve in the Gulf War.
b- What was the likely effect of this failure on relative risk? Discuss your train of thoughts and rationale.

Question 3:
A journalist looking into ‘tutoring business’ has gathered some interesting data. She has been able to obtain a list of students of one of the middle schools, who received private tutoring in the previous year, and compared their marks with the marks of the students of the same school, who did not receive private tutoring. Interestingly, she discovers that there is a strong negative association between receiving tutoring and performance of the students; i.e. the more tutoring they receive, the less their marks are. She concludes that tutoring is in fact harmful to the academic performance of students rather than being helpful.
Based on what you have learned in this course so far, analyze this study and the conclusion that was drawn from it. Your analysis must at least include:
- Analysis of internal and external validity of this study
- Hypotheses of possible confounding factors that may have played a role here
- Discussion of what other studies can be performed to help test your hypotheses, as well as help confirm or reject the conclusion of this study (also discuss their design).

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These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

1- Necessary but not sufficient, because there is no Hepatitis B without the virus, but one can have the virus without Hepatitis B.
2- Not necessary and not sufficient, because not all gastric ulcer patients have...

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