Question

the table below shows the conditional relative frequencies of a set of data comparing gender and whether an academic scholarship was earned. \

$$\begin{tabular}{|c|c|c|c|} \\hline & \\multicolumn{1}{|c|}{scholar- ship} & \\multicolumn{1}{|c|}{no scholar- ship} & \\multicolumn{1}{|c|}{total} \\\\ \\hline male & 0.47 & 0.53 & 1 \\\\ \\hline female & 0.52 & 0.48 & 1 \\\\ \\hline total & 0.495 & 0.505 & 1 \\\\ \\hline \\end{tabular}$$

which conclusion can be drawn from the table? \bigcirc an association cannot be determined because 0.47 is close to 0.52. \bigcirc there is an association between gender and scholarship earned because each row adds to 1. \bigcirc an association cannot be determined because 0.47 is close to 0.53. \bigcirc there is an association between gender and scholarship earned because each column total is the average of the values in the column.

Explanation:

To determine the association between gender and scholarship earned, we analyze the conditional relative frequencies. For males, the frequency of earning a scholarship is 0.47 and not earning is 0.53. For females, it's 0.52 (scholarship) and 0.48 (no scholarship). The difference in these proportions (e.g., 0.47 vs. 0.52 for scholarship) shows a noticeable variation between genders. The option stating an association exists because column totals are averages (since 0.495 is the average of 0.47 and 0.52, 0.505 is average of 0.53 and 0.48) indicates a relationship, as the proportions differ by gender. Other options are incorrect: the first two reasons (closeness or row totals) don't justify no association, and row totals adding to 1 is standard for conditional relative frequencies, not an association indicator.

Answer:

There is an association between gender and scholarship earned because each column total is the average of the values in the column.