[Math] Relative frequency – Basic stats

data analysisstatistics

There's this practice problem in Khan Academy (Statistics and Probability)

Justin's dad claims that taking piano lessons will help Justin get into an Ivy
League school one day. Justin decides to try to prove his dad wrong by interviewing a randomly selected sample of college-educated adults. Justin asks them whether they
attended an Ivy League school and also whether they took piano lessons as a child.

The relative frequency table (image attached) shows his results. Justin interviewed $9$ randomly selected adults who attended an Ivy League school but did not take piano lessons.

Does the table show evidence of an association between not taking piano lessons and not attending an Ivy League school?

From the table, the joint relative frequency for people who did not take piano lessons and who did not attend an Ivy League school is the greatest. Am I right in assessing that these two are associated?

relative frequency table

Best Answer

To get those numbers, he is more likely to have interviewed $48$ people (or some multiple) than $9$, since for example only $2.1\%$ said they were Ivy League piano players. In some cases the actual numbers matter.

You should be thinking about questions like:

  • What proportion of piano players were Ivy Leaguers?
  • What proportion of non-piano players were Ivy Leaguers?
  • Is the difference significant? (There are tests you can use such as the chi-square test or Fisher's exact test, though the answer here is obvious with these values)
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