We will begin by looking at the given two-way table and the conclusion that was made about it. We are asked to describe and correct the error in using the two-way table.

The given statement says that the table shows the joint relative frequencies. A joint relative frequency in a two-way frequency table is the ratio of a joint frequency and the total number of values or observations. Let's find the total number of observations by adding the joints frequencies, which are the numerators of the given ratios.

187 + 85 + 123 + 93 = 488

Looking at the table, we can see that every entry is not divided by the total number of observations, so the table does not show joint relative frequencies. Additionally, it seems that the entries of the table are divided by the marginal frequencies. A marginal frequency is the sum of the row or column of joint frequencies. Let's find the marginal frequency for each row.

Freshman : Sophomore : 187 + 85 = 272 123 + 93 = 216

We can now see that each entry in the table is the ratio of the joint frequency to a marginal frequency, which is the definition for a conditional relative frequency. Therefore, the two-way table shows conditional relative frequencies. Let's correct the given statement.

Exercise

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