Math 1100, Section 3



Midterm Review


Producing data

  1. Sample question: What is an observational study? An experiment? What are the chief differences between these ways of acquiring data? How does a case-control study differ from an experiment?
  2. Be able to classify examples as to whether they are studies or experiments and explain why. Be able to read and comment on a newspaper clipping.
  3. Sample question: How are samples used to obtain information about populations? Give examples. What kinds of things does a statistician need to be careful with when making inferences from samples?

The concept of a variable

  1. Sample question: Write a short paragraph explaining the following terms: variable, measurement, reference class, set of possible values, qualitative, quantitative. OR: Make a concept map involving these terms.
  2. Be able to recognize variables in newspaper stories and pick out the kind of variable, reference class, measurement method.
  3. Be able to give numerous examples.

The concept of a distribution

  1. Sample question: What is meant by the "distribution" of a variable?What does this have to do with the idea of a frequency table? A table of relative frequencies?
  2. Be able to provide examples of distributions.
  3. Given a data set, be able to make make a table of frequencies, relative frequencies. Be able to draw bar charts and/or pie charts to show a distribution.
  4. Be able to comment on bar charts and pie charts and answer questions such as: What is the value this variable assumes most frequently? What is the range of the distribution (i.e., highest and lowest values)? What is the average value of the following distribution:
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  1. Be able to give many examples of processes that produce random data
  2. Sample question: What is the "Law of Large Numbers?"
  3. Sample question: One version of the law of Large Numbers says "If you wait long enough, even unlikely things happen." Another version says, "In a large number of repetitions of a probabilistic experiment, the relative frequency of an outcome will be close to its probability." How are these two statements related?
  4. Sample question: A gambler begins the evening with an unusually bad loss. What is the more intelligent action, and why? 1) Leave the casino and eat the loss. 2) Continue playing, figuring that by the Law of Large Numbers, he can expect to balance the loss.
  5. Sample question: What is meant by "statistical significance"?

Probability Models

  1. Sample question: Explain the terms: probabilistic experiment, outcome, event, sample space, probability of an event. OR Draw a concept map involving these terms.
  2. Given some examples of probabilistic experiments (e.g., flip 5 coins, roll 3 dice, etc.), describe the sample space and name the outcomes in selected events (e.g., what outcomes are in the event: "flipped more heads than tails" or "rolled a sum of 10")
  3. Interpret probability as relative frequency.
  4. Be able to draw the tree diagram for the experiment of taking beads (of some specified number and color) from a jar, with or without replacement.

Probability Problems

  1. If a die is tossed 4 times, what is the probability that neither a 5 nor a 6 ever appears? (See the discussion at Note 1.)
  2. If a wall is painted 1/2 red, 1/3 green and 1/6 blue and 3 darts are thrown at the wall at random, what is the probability that at least one dart lands in green?
  3. If a coin is tossed 5 times, what is the probability that exactly two heads appear?
  4. In a given town, 1/4 of the people are democrat and 3/4 are republican. One in 4 is black and the remaining citizens are white. If 1 in 8 is a black republican, then what proportions are the other possibilities? Is race associated with political party?
  5. A bead problem, such as that in Note 2.