15E Coreq

In the next preview assignment and in the next class, you will need to read contingency tables and be able to logically combine cells of contingency tables. Organizing Categorical Bivariate Data A teacher asks a group of 11 students the following questions:
•Do you have a driver’s license? •Do you own a bicycle? The answers are recorded asfollows:
Driver’s License? Bicycle?
Student 1 Yes Yes
Student 2 Yes No
Student 3 No Yes
Student 4 No Yes
Student 5 Yes No
Student 6 No No
Student 7 No Yes
Student 8 Yes Yes
Student 9 Yes No
Student 10 Yes Yes
Student 11 No Yes

Question 1

1) Is the variable Do you have a driver’s license categorical or quantitative?

Question 2

2) Is the variable Do you own a bicycle categorical or quantitative? From looking at this table, it might be difficult to get a good sense of any patterns in the dataset. The teacher decides to organize the information into a contingency table. Previously, you have used this tool to organize bivariate, categorical data. In each cell, there is an integer, representing a frequency or count.

Question 3

3) Fill in the cells in the following table, using the labels as a guide.

Yes, has a driver’s license No, does not have a driver’s license
Yes, owns a bicycle
No, does not own a bicycle

Question 4

4) How many students have driver’s licenses but do not own bicycles?

Question 5

5) In a sentence, explain what the number four represents in the previous table. Contingency tables are particularly useful when datasets are large. Consider the following example.

Questions 6–10: On March 23, 2021, S.937: COVID-19 Hate Crimes Act was presented to the United States Senate, the purpose of which is to “facilitate the expedited review of COVID-19 hate crimes, and for other purposes.”[1] On April 22, 2021, it passed in the Senate. The votes on the bill are in the following table.
Republicans Democrats Independents
Yes 46 46 2
No 1 0 0
Not Voting 3 2 0

Question 6

6) How many people did not vote on the bill?

Question 7

7) How many senators are not Republicans?

Question 8

8) How many senators are Democrats or Independents?

Note that the answers to Questions 7 and 8 are the same! Asking about a person not being a Republican is the same as asking if they fit into the Democrat or Independent category!

Question 9

9) In a sentence, explain what the number three in the previous table represents.

Question 10

10) Suppose that a researcher wanted to reorganize the data with different labels. Fill in the following table, using the labels as a guide.
Republicans Other
Yes
Other

Question 11

11) Using the answer to Question 10, how many senators are not Republicans? Note that Questions 7 and 11 are the same, as are the answers. Reorganizing the data will not change the answer to a question—but it does change what questions we can answer!

Question 12

12) A physician organizes her practice’s patient database based on their ages and the frequency of weekly exercise that they report to do. The following table describes the data.
20–29 years 30–39 years 40–49 years 50–59 years 60–69 years 70–79 years 80–89 years
0–1 days per week 7 12 55 40 30 4 9
2–4 days per week 35 41 45 50 55 30 12
5–7 days per week 31 44 49 40 24 12 1
Part A: Collapse the frequency counts in this dataset as indicated by the labels in the following table.
20–49 years 50–89 years
0–1 days per week
2+ days per week
Part B: Would it make sense to collapse the cells as indicated in the following table? Explain.(Note: Do not fill in the table, just consider the labels to answer the question).
20–29 and 70–89 years 30–69 years
0–1 days per week
2+ days per week
Part C: Determine whether this statement is true or false:The total sum of frequencies changes when cells are collapsed.
  1. GovTrack. (2021, May 19). S.937: COVID-19 Hate Crimes Act.https://www.govtrack.us/congress/bills/117/s937/text ↵