MATH 2565 W 2014/More sample midterm questions

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NATS 1500 exam from last year (

More sample midterm question for MATH 2565

  1. Why does Hans Rosling say that students at the Karolinska Institute know statistically significantly less about the world than do chimpanzees -- and professors at the Karolinska Institute are roughly on a par with chimpanzees?
  2. Use an Agresti diagram to explain how conditional association between two variables can have a different sign than their unconditional association: You would be asked to do this with a specific example, e.g. quitting smoking and health, using sunscreen lotion and skin damage, working more hours per week and getting higher grades. In each case you want to identify a plausible confounding factor and draw the Agresti diagram conditioning on levels of the confounding factor.
  3. A study showed (this is true) that students who view the recorded videos of the lectures many times perform less well on the final exam than students who view the videos fewer times. Upon discovering this, your professor announces that he/she will discontinue recording the lectures because, the professor says, the videos have been shown to cause students to do perform more poorly on the course. Explain your point of view to the professor -- in clear and simple language even a professor might be able to understand.
    • Explain why the number of lectures attended could be a potential confounding factor in considering the relationship between the frequency of viewing class videos and performance on the course.
    • Can you think of potential mediating factors?
  4. In the 1964 U.S. Public Health Service study it was found that, for men and for women in each age group, current smokers were on average much healthier than the former people who had quit smoking.
    • Suppose that an important factor that explains this surprising fact is that people who quit smoking tend to experience increased stress and weight gain as a result of quitting, and that these factors adversely affect health. Are increased stress and weight gain potential mediating factors or confounding factors? Explain briefly.
    • Suppose that an important factor that explains this fact is that an important proportion of people who quit smoking do so because they are in poor health and have been strongly advised to quit smoking by their physicians. Would this be a mediating factor or a confounding factor in considering the relationship between between quitting smoking and health? Explain briefly.
    • In this study, are age and sex potential confounding factors or mediating factors?
  5. A study shows that heavy users of sunscreen lotion have a higher chance of developing skin cancer.
    • Does this imply that you should avoid using sunscreen lotion in order to reduce your chances of developing skin cancer?
    • A friend who has never studied statistics asks your advice. She wants to know whether she should stop using sunscreen lotion when she goes outside on a sunny day. What would you say to her?
    • Can you think of potential confounding factors and potential mediating factors?
    • Draw an Agresti diagram that could apply to this example.
  6. What 3 conditions ensure that a random variable X would have a distribution that is close to a normal distribution?
  7. Given a 2x2 table, answer a question that involves interpretation of row or column percentages as appropriate. e.g.
    • In a sample of 1000 21-year-old drivers, 10% had accidents in the past year and 90% did not. Of those who had accidents, 20% had had driver education and of those who had not had accidents, 60% had had driver education.
      1. Construct a 2x2 frequency table to classify the sample according to whether each unit had driver education and/or accidents.
      2. How does the risk of having an accident vary depending on having had driver education?