IM3.7.2 Two way tables (TWT)
The school board of Waldo, a small town in America, is considering building a new high school primarily funded by local taxes. They decided to interview eligible voters to determine if the school board should build a new high school facility to replace the current high school building. There is only one high school in the town. Every registered voter in Waldo was interviewed. In addition to asking about support for a new high school, data on gender and age group were also recorded. The data from these interviews are summarized in the table below.
1. Based on this survey, do you think the school board should recommend building a new high school? Explain your answer.[br]2. An eligible voter is picked at random. If this person is 21 years old, do you think he would indicate that the town should build a high school? Why or why not?[br]3. An eligible voter is picked at random. If this person is 55 years old, do you think she would indicate that the town should build a high school? Why or why not?[br]4. The school board wondered if the probability of recommending a new high school was different for different age categories. Why do you think the survey classified voters using the age categories 18–25 years old, 26–40years old, 41–65years old, and 66 years old and older?
Make a TWT
5. It might be helpful to organize the data in a two-way frequency table. Use the given data to complete the following two-way frequency table. Note that the age categories are represented as rows, and the possible responses are represented as columns.
Critiquing the reasoning of others
6. A local news service plans to write an article summarizing the survey results. Three possible headlines for this article are provided below. Is each headline accurate or inaccurate? Support your answer using probabilities calculated using the table above. [br]Headline 1: Waldo Voters Likely to Support Building a New High School[br][br]Headline 2: Older Voters Less Likely to Support Building a New High School[br][br]Headline 3: Younger Voters Not Interested in Building a New High School
Using probability to make decisions
7. The school board decided to put the decision on whether or not to build the high school up for a referendum in the next election. At the last referendum regarding this issue, only 25 of the eligible voters ages 18–25 voted, 110 of the eligible voters ages 26–40 voted, 130 of the eligible voters ages 41–65 voted, and 80 of the eligible voters ages 66 and older voted. If the voters in the next election turn out in similar numbers, do you think this referendum will pass? Justify your answer.[br][br]8. Is it possible that your prediction of the election outcome might be incorrect? Explain.