Question

# One hundred adults and children were randomly selected and asked whether they spoke more than one language fluently.

Two-way tables
One hundred adults and children were randomly selected and asked whether they spoke more than one language fluently. The data were recorded in a two-way table. Maria and Brennan each used the data to make the tables of joint relative frequencies shown below, but their results are slightly different. The difference is shaded. Can you tell by looking at the tables which of them made an error?

2021-07-27

We determine the marginal relative frequencies using Maria's table:

$$\begin{array}{c|c}&Yes&No&\text{Total}\\\hline\text{Children}&0.15&0.25&0.40\\\hline\text{Adults}&0.1&0.6&0.7\\\hline\text{Total}&0.25&0.85&1.1\end{array}$$

We determine the marginal relative frequencies using Brennan's table:

$$\begin{array}{c|c}&Yes&No&\text{Total}\\\hline\text{Children}&0.15&0.25&0.40\\\hline\text{Adults}&0.1&0.5&0.6\\\hline\text{Total}&0.25&0.75&1.0\end{array}$$

Maris's table is wrong because the number in the lower right cell is not 1. Brennan's table is correct.

Result: Maria's table