Question

The following partially completed two-way table shows the marginal distributions of gender and handedness for a sample of 100 high school students.

If there is no association between gender and handedness for the members of the sample, which of the following is the correct value of x?

(a) 20

(b) 30

(c) 36

(d) 45

(e) Impossible to determine without more information.

Short answer

Option (c) 36 is the correct option.

Step-by-step solution

Step 1. Given information.

The given table is:

Step 2. Explanation for the correct option.

If there is no link between gender and handedness, the value in a table cell should be equal to the product of the row and column totals, divided by the table total, because the proportion of right-handed people must be the same for males and the overall population.

$$\begin{gathered} x=\frac{\mathrm{Row}\mathrm{total}\mathrm{x}\mathrm{Column}\mathrm{total}}{\mathrm{Table}\mathrm{total}} \\ =\frac{90\times 40}{100} \\ =\frac{3600}{100} \\ =36 \end{gathered}$$

As a result, answer choice (c) should have a value of 36.