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Recall the definition of a two-way table.
See solution.
We want to describe how we can use two-way tables to find possible associations between two different categories from the same sample group. To answer the question, let's consider an example.
The two-way table below shows the results of a survey where 100 participants were asked if they were raised in a city and if they can swim.
Let's take a closer look at the results. From the table we can read that 0.02 or 2% of the people who were not raised in a city cannot swim.
To decide if there is an association between being raised in a city and being able to swim, we should look at the first column of the table. Out of the people who were raised in a city, 0.54 or 54% can swim. Also, 0.98 or 98% of the respondents who did not grow up in a city can swim.
Since 0.98>0.54, a person who was not raised in a city is more likely to be able to swim. In other words, there is an association between being raised outside of a city and being able to swim.
If we calculate and then compare the relative frequencies in the two-way table, we can see if a member of one category is more likely to fall into the other category. In this case, we found that respondents who were raised outside a city were more likely to be able to swim.