standard_description: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
problem_activity: Task
Ari has collected data on how much her classmates study each week and how well they did on their recent math test. Here is part of the data, showing the percentage of each group (divided according to hours spent studying) who got different grades on the test:
{"table": [{"_attributes": {"class": ["regular"]}, "tbody": [{"tr": [{"th": [{"_value": "Weekly Hours $w$ Studying"}, {"_value": "C or below on test"}, {"_value": "B on test"}, {"_value": "A on test"}]}, {"td": [{"_value": "$w \\lt$ 3"}, {"_value": "50%"}, {"_value": "20%"}, {"_value": "30%"}]}, {"td": [{"_value": "$3 \\leq w \\lt 6$"}, {"_value": "60%"}, {"_value": "25%"}, {"_value": "15%"}]}, {"td": [{"_value": "$w \\geq 6$"}, {"_value": "60%"}, {"_value": "20%"}, {"_value": "20%"}]}]}]}]}
What can you conclude about the percentage of Ari's classmates who got B's? What about the percent who got A's?
Looking at the table, Ari decides that in order to do well in her math class, she should not study more than 3 hours a week: she has a 30 percent chance of getting an A as long as she does not study more than 3 hours per week. Is Ari's reasoning valid?


aligns: no