Political polls do a remarkably good job of predicting the winner of national elections. However, we occasionally hear of a case where a poll has gone badly wrong. An example illustrating this was the 1992 election in Colorado, where a measure was on the ballot to prohibit the state legislature and cities from passing anti-discrimination laws concerning homosexuals. Polls showed that the Colorado measure would be defeated. The measure passed (See the New York Times, November 8, 1992).

Question: What may have accounted for the difference between the result in the polls and the result in the election? In this activity you will examine how the design of a survey can affect the answers that are given.

Activity: Within your group, pick a topic of interest to you and design a binomialexperiment with a questionnaire that contains about 5-10 items about this topic. Give the questionnaire to people and have them complete it (no convenience sampling!). Use the students at school as the population of interest. Before doing the survey, your group will have to decide upon a sample size that will be large enough to establish the statistical significance of any difference you feel is practically significant.

After getting feedback from these people, change the questions. Then pick a random sample of people from an appropriate population and have them answer your next set of questions. This means you will have two questionnaires – one that is straight-forward and one that has been changed somehow in order to observe how the variable you introduced will change the outcome of the experiment.

Examples of ideas for simple experiments:

  1. Does the order in which 2 candidates appear on a ballot make a difference in the percentages of votes they receive?
  2. Is it possible to word a question in 2 different ways that are logically equivalent but that have a different percentage of students agree with them?
  3. Does the order in which 2 statements appear in a survey make a difference in the percentage of students who agree with them?
  4. Can the percentage who agree with a statement be changed by having respondents read some introductory material?
  5. If a statement is rewritten to be logically equivalent but to have a more complicated sentence structure and bigger words, will it affect the percentage of students who agree with it?
  6. Does the appearance of the interviewer make a difference in how students will respond to a question? For ex, do students tend to respond the same way about a controversial issue when the interviewer is a female as when the interviewer is male?
  7. If the interviewer does not know how a student responds (as on a secret ballot), does it make a difference in the percentage of students who agree with a controversial statement?
  8. If a student knows absolutely nothing about an issue, will he or she give an opinion anyway? Will students admit if they don’t know the answer to a question?
  9. Do students report events (such as how many days last week had rain or the description of a person who just walked by) as accurately as they think they do?
  10. If you let students volunteer to be in your poll, do you get a different result than if you approach students?

Wrap Up: Analyze and summarize the results of both sets of data using your knowledge of binomial distributions with the details outlined in the following rubric.Your group should prepare a report about what you have learned and present it to the rest of the class (PowerPoint or video only). Make sure you include an introduction, analysis, and conclusion.

Group Names:______Topic: ______

Date: ______Total Time: ______Presentation: ____/60 per person

Time: ____/10

(8-10 Minutes per group)

Presentation: ____/10

a)Evidence of preparation/ Clear understanding of the topic(s) (1pt)

b)Equal participation by each member of the group (1pt)

c)Appropriate aids which support the presentation (PowerPoint or video) (1pt)

d)Creativity (1pt)

e)Clear explanation or review of the material (via introduction, analysis, and conclusion) (3pts)

f)Informative/Educational (1pt)

g)Attach a survey; environmentally-friendly? (Save paper!) (2pts)

Content (demonstrate appropriate problems): ____/30

a)Why did you pick your topic? (1pt)

b)Explain how you got your sample (randomization technique); list the teachers (1pt)

c)Show survey given (1 pt)

d)Was your sample size big enough? How do you know? (1pt)

e)Graphically analyze each question’s results; compare and contrast biased vs. unbiased questions (10 pts)

f)Check the requirements for a binomial distribution are met (4pts)

g)Ask/answer a probability question using your nonbiaseddata for each question; illustrate all 3 methods of calculating Binomial probabilities (formula, table, software). (3pts)

h)Interpret what these probabilities mean. Are the results unusual? (1 pts)

i)Correct notation used? (Identify values of n, x, p, and q) (1pt)

j)Find the mean, variance, standard deviation of each question (5pts)

k)Can you draw any conclusions? How did the construction of the questionnaire affect your results? (1pts)

l)If you were to repeat this survey, what would you change? (1pt)

Presence: ____/10

a)Posture, stance, gestures, eye contact (no sitting) (1pt)

b)Speech (tone/volume, enunciation, minimal ahs, ums, etc) (1pt)

c)Command/confidence/ Effective use of notes/visual aids (2pts)

d)Enthusiasm/positive approach/attitude (humor okay; silliness not) (1pt)

e)Present for all presentation days (2.5pts/day)