Question

A teacher collected data from a class of eighth grade students on whether or not they have a sister and whether or not they have a brother. The two-way table below shows the data collected.

A teacher collected data from a class of eighth grade students on whether or not they have a sister and whether or not they have a brother. The two-way table below shows the data collected.

Sister No Sister Total
Brother 5 12 17
No Brother 9 4 13
Total 14 16 30

Calculate the relative frequency of the data to determine which association the two-way table suggests.
A.
Those who have a brother tend not to have a sister.

B.
Those who do not have a brother tend not to have a sister.

C.
Those who have a brother tend to have a sister.

D.
None of the associations listed are correct.

Answer 1

B. Those who do not have a brother tend not to have a sister.

Explanation:

To determine the relative frequency of the data in the two-way table, we need to calculate the proportion of each category in relation to the total number of students.

First, let's calculate the relative frequencies for each category:

Relative frequency of having a sister and a brother:

5 (students with sister and brother) / 30 (total students) = 1/6 ≈ 0.1667

Relative frequency of having a sister but no brother:

12 (students with sister but no brother) / 30 (total students) = 2/5 = 0.4

Relative frequency of having a brother but no sister:

9 (students with brother but no sister) / 30 (total students) = 3/10 = 0.3

Relative frequency of having neither a sister nor a brother:

4 (students with no sister and no brother) / 30 (total students) = 2/15 ≈ 0.1333

Now, let's analyze the relative frequencies to determine the association suggested by the two-way table.

The highest relative frequency is for the category "Those who have a sister but no brother" with a relative frequency of 0.4. This suggests that the most common association in the data is that "Those who do not have a brother tend not to have a sister." Therefore, the answer is:

B. Those who do not have a brother tend not to have a sister.