Randomness Quiz

INSTRUCTIONS:

On this test, the number of asterisks at the beginning of each question indicates what level of knowledge/difficulty each question assesses. Once an answer is chosen, a function is called which scores the question according to the following table:

Question
level
full
credit
partial
credit
level 3 = ***85
level 2 = **63
level 1 = *42

Scroll down to the first question below. Notice that to the left of the "c" button is a rectangular button called "hint". This indicates that you can click on that button to receive a hint about this question (not just the "C" choice). If the button is blank, there is no hint available for that question. If there is a hint avaliable for a question, and you use it before answering, one point is subtracted from the points above. Thus, if you are fairly confident of the answer, you should ignore the hint. But if you are uncertain of the answer, using the hint should help you earn more points in the long run.

Once you have decided on the best answer, click on the radio button to the left of the letter representing your answer. Then you can click on the "correct?" button to receive immediate feedback about whether you were correct, how many points you earned on that question, and an explanation of the correct reasoning. This information will be printed in the "white windows."

To the left of the explanation window, there may be a "link" button displayed. If so, you can jump to material directly related to the question content which you can review to solidify your understanding of the explanation. If the button is blank, there is no link.

You do NOT have to do the questions in order, and you can attempt any questions you wish.

Here are some short answer essay questions you should be able to answer:

Level 1:

  • What are two reasons why people have such a hard time responding in a random fashion:

    answer

  • Explain what a scientist means my the statement: "Before we explain something we must give chance a chance!"

    answer

    Level 2:

  • Explain how misunderstanding randomness can lead to superstitious behavior:

    answer

  • Cluster illnesses occur when people notice clusters of illnesses in their neighborhoods such as cancer, birth defects, etc. and attribute it to environmental pollution, government conspiracies, or even evil spirits. How can the hot hand and randomness fallacies explain why people believe in "cluster illnesses?" Write your answer in the box below.

    answer

    Level 3:

  • No baseball player since Ted Williams in the 1950's has finished the season with a batting average above .400. Suppose Joe Blow¹s average is .428 at the All Star break (season half-way point). Why would a baseball fan NOT be in error to say that Joe Blow is due for a long HITLESS streak which will pull his average below 400?

    answer

  • End of Quiz

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Problems:

    1. Because we have memories (for our past behaviors). We have to ignore our past in order to respond randomly.

    2. We really don't know what random means, and it is not taught to us in school. So we don't know how to act. Our misconceptions cause us to act 'badly.'

    3. we have preferences for certain behaviors, we have styles. We like to do things a certain way, and, unless we are exceptionally vigilant, it will be hard to suppress these preferences.
    4. the need for control feeds the illusion that we can control or predict chance events. To acknowledge a random world decreases our sense of power and prediction.
    5. In everyday experience, we may not encounter that many randomly determined events, or the random events are hidden from us.
    6. Finally, maybe our deterministic, cause-effect, thinking style keeps our minds from understanding the concept of randomness.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      >Giving chance it's due: Before we accept any event as unsual or a potential cause for something else, we have to rule out the possibility that the event is a random event or is unrelated to the effect. Scientists do that because they believe in the "law of parsimony," that they should accept the simplest, least complicated explanation for something. That explanation is that the event is due to chance.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

      Supersitition:They may wrongly infer that a series of repeating events is a streak of good/bad luck because they underestimate how often chance events can re-occur. Second, they could underestimate the likelihood that chance could produce a given outcome (such as thinking of someone and then having the person call you), so they attribute great significance to it. Third, they can develop an illusory correlation between some action they perform and repeated events, not realizing that by chance alone, some actions will always co-occur with the events.

     

     

     

     

     

     

     

     

     

     

     

     

     

      Cluster: People don't realize that uncommon events will repeat themselves more often than they realize. So when 5 babies are born in one day with a birth defect, people look for a cause. Although there might be cause, it could be a random event that will happen once and a while by chance alone, Given the number of babies being born, and the media's tendency to pick up on such coincidences, we will hear of them.

    Level 2 and 3 elaboration:

    For example, if the birth defect rate is 1 in 100, then according to the binomial formula, the chance of getting at least 6 defects out of 10 births is .001. Across the many hospitals in America, there will be many brief periods of time when at least 10 babies are born. In a given year, if there were 10,000 such periods, we would expect to find 10 such clusters by chance alone.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Hitless:

    Hitting above 400 is a very unusual event, so it is likely to regress to more typical levels over time. Thus, due to regression towards the mean, the average for the second half of the season will be less extreme than was the first half. This can only happen if Joe Blow has some hitless streaks. Although hitting a baseball is not a chance event, there is an element of chance along with a batter's skill level. During the first half of the season, there were probably more "lucky breaks" than normal, producing such an unusually high average. It is unlikely that the same abnormal level will occur in the second half.