standard_description: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
problem_activity: Task
The 54 students in one of several middle school classrooms were asked two questions about musical preferences: “Do you like rock?” “Do you like rap?” The responses are summarized in the table below.
{"table": [{"tbody": [{"tr": [{"td": [{}], "th": [{"_value": "Likes Rap"}, {"_value": "Doesn't Like Rap"}, {"_value": "Row Totals"}]}, {"th": [{"_value": "Likes Rock"}], "td": [{"_value": "27"}, {"_value": "6"}, {"_value": "33"}]}, {"th": [{"_value": "Doesn't Like Rock"}], "td": [{"_value": "4"}, {"_value": "17"}, {"_value": "21"}]}, {"th": [{"_value": "Column Totals"}], "td": [{"_value": "31"}, {"_value": "23"}, {"_value": "54"}]}]}]}]}
Is this a random sample, one that fairly represents the opinions of all students in the middle school?
What percentage of the students in the classroom like rock?
Is there evidence in this sample of a positive association in this class between liking rock and liking rap? Justify your answer by pointing out a feature of the table that supports it.
Explain why the results for this classroom might not generalize to the entire middle school.


aligns: no