In January 1971, a Gallup Poll asked, "A proposal has been made in Congress to require the US government to bring home all US troops before the end of the year. Would you like to have your congressman vote for or against this proposal?"
This is a real poll that was given during the Vietnam War. Please don't peek at the actual poll results ahead of time. I'll share them at the end of the session.
|
Grade School Education
|
High School Education
|
College Education
|
All Adults
|
|
% for withdrawal
|
|
|
|
73%
|
|
% against withdrawal
|
|
|
|
27%
|
|
Total
|
100%
|
100%
|
100%
|
100%
|
Guess the results for respondents in each education category, and fill out the table. Why did you guess the numbers you did?
The politics involved regarding this topic can get a bit heated, but the main idea behind the conference is to test your understanding of basic concepts regarding probability tables. Here are some tips to keep in mind as you complete your chart:
All of the people polled are adults. The education levels mentioned here refer to the highest level that poll participants completed in school, not their ages when answering the poll.
In addition to the columns totaling 100%, the values you use in each row have to roughly average the row totals. That means that the numbers that you use in each row should roughly average the percentage in the final column of that row. Your responses in row one need to roughly average 73%. Why? Because, in the absence of additional information, we assume that the same number of people were polled in each category.
Optional: If you were successful above, now, convert your table from one based on column percentages to one based on percentage of the overall total. You will have to use the values from your first table to accomplish this. I'll get you started. Your column entries will now sum to the column totals. Your row entries will sum to the row totals.
|
Grade School Education
|
High School Education
|
College Education
|
All Adults
|
|
% for withdrawal
|
|
|
|
73%
|
|
% against withdrawal
|
The value here is your % from the above chart times 34%
|
|
|
27%
|
|
Total
|
34%
|
33%
|
33%
|
100%
|
To truly test your understanding of this week's material, once you have completed your table, see if you can answer questions like...
- Which events in the table are simple events?
- Which events in the table are joint events?
- Which values represent marginal probabilities?
- What is the probability that a respondent is against withdrawal and a high school graduate?
- What is the probability that a respondent is college educated, given that he is for withdrawal?
- Are any of war positions independent of education level?