standard_description: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
problem_activity: Task
Each student in a random sample of students at a local high school was categorized according to gender (male or female) and whether they supported a proposal to increase the length of the school day by 30 minutes (oppose, support, no opinion). The following table summarizes the data for this sample.
{"table": [{"tbody": [{"tr": [{"td": [{"_attributes": {"colspan": "2", "rowspan": "2"}, "p": [{}]}, {"_attributes": {"colspan": "4"}, "p": [{"_value": "Opinion on Proposal to Increase Length of School Day"}]}]}, {"td": [{"p": [{"_value": "Oppose"}]}, {"p": [{"_value": "Support"}]}, {"p": [{"_value": "No Opinion"}]}, {"p": [{"_value": "Total"}]}]}, {"td": [{"_attributes": {"rowspan": "3"}, "p": [{"_value": "Gender"}]}, {"p": [{"_value": "Male"}]}, {"p": [{"_value": "50"}]}, {"p": [{"_value": "40"}]}, {"p": [{"_value": "20"}]}, {"p": [{"_value": "110"}]}]}, {"td": [{"p": [{"_value": "Female"}]}, {"p": [{"_value": "40"}]}, {"p": [{"_value": "40"}]}, {"p": [{"_value": "10"}]}, {"p": [{"_value": "90"}]}]}, {"td": [{"p": [{"_value": "Total"}]}, {"p": [{"_value": "90"}]}, {"p": [{"_value": "80"}]}, {"p": [{"_value": "30"}]}, {"p": [{"_value": "200"}]}]}]}]}]}
What proportion of the students in this sample are male?
What proportion of the students in this sample support the proposal?
What proportion of the males in this sample support the proposal?
What proportion of the students in this sample who support this proposal are male?
Interpret the following joint relative frequency in the context of this problem: 10/200.
Interpret the following marginal relative frequency in the context of this problem: 30/200.
Interpret the following conditional frequency in the context of this problem: 50/110.
Interpret the following conditional frequency in the context of this problem: 20/110.
Interpret the following conditional frequency in the context of this problem: 20/30.


aligns: no