Math 124.05

Midterm II Answers

November 6, 2007

You may use one page of notes, a calculator and a normal table. If you want to use a computer, please check with me first. You may ask questions during the test.

  1. What is the difference between observational and experimental studies? Explain some of the advantages and disadvantages of each.
  2. An observational study is one in which the researcher observes subjects behaving naturally. The research does not influence the behavior of the subjects in any way. The most important advantage of observational studies is that the subjects behavior is natural and not influenced by the researcher. Another advantage of observational studies is the possibility of observing subjects behaving in ways that it would be unethical to ask them to behave. The disadvantages include the inability of the researcher to control for lurking variables.
    An experimental study is one in which the researcher asks subjects to engage in certain behaviors or undergo certain treatments. Subjects are assigned at random to the different groups. The advantage of this type of study is that the researcher can control for lurking variables and perhaps distinguish more precisely than in an observational study the effects of different behaviors or treatments. The disadvantage of experimental studies, particularly for behavioral studies, is that the subjects are not behaving naturally. Another disadvantage is that subjects may not follow the assigned protocol exactly.
  3. Describe two types of improper survey questions.
  4. A leading question is one that includes information (which may or may not be accurate) or phrasing designed to affect the subject's response. Example: Do you think we should make our streets safer by raising the driving age to 25?
  5. A sensitive question is one that subjects may be unwilling to answer honestly, for example: Have you caused an auto accident in the past year?
  1. Suppose you have an unbalanced coin and the probability of heads is P(H) = 0.6. Let X be the random variable that is the number of heads in 200 tosses.
  2. What is the distribution of X—binomial, normal, uniform or other?
  3. X has a binomial distribution.
  4. What are the mean and standard deviation of X?
  5. The mean is . The standard deviation is
  6. What is the probability that, out of 200 tosses, more than 133 heads occur.
  7. Let be the normally distributed random variable that approximates X. (We can approximate X with a normal variable because np=120 and n(1-p)=80 are both greater than 10.) Then the mean of is 120 and the standard deviation of is 6.93. We can calculate the probability that there are more than 133 heads in 200 tosses:
  1. If A and B are events, and P(A) = .25, P(A and B) = .1 and P(A or B) = 0.4, find P(not B). Explain your reasoning.
  2. Since

    we have
  3. A group of students was surveyed about ear piercings with the following results:

pierced / not pierced / total
male / 36 / 144
female / 288 / 32
total

What is the probability that a random student has pierced ears or is male or both?

The number of students who are male or have pierced ears is 36+144+288 = 468. The total number of students is 500, so the probability that a random student is male or has pierced ears is

  1. Foot length for men has a mean of 10" and a standard deviation of 2" (numbers I just made up). Let X be the random variable that is the average foot length of a random sample of 100 men.
  2. What is the distribution of X—binomial, normal, uniform or other?
  3. By the Central Limit Theorem, X has a normal distribution.
  4. What are the mean and standard deviation of X?
  5. The mean of X is the same as the population mean, 10”, and the standard deviation of X is the standard deviation of the population divided by the square root of the sample size:
  6. Five percent of all samples have average foot length longer than what length?
  7. The question asks you to find x, where P(X > x) = 0.05. From the table,
    P(Z > 1.64) = 0.05 , so x = 10 + 1.64(0.2) = 10.3”