Consider the proportion of "successes" \( \hat{p}=\frac{27}{28} \). (a) In fraction form, what is the proportion of failures, \( (1-\hat{p}) \) ? (b) Choose the correct inequality to compare the two proportions.

The proportion of failures can be calculated by subtracting the proportion of successes from 1. So, we have \( 1 - \hat{p} = 1 - \frac{27}{28} = \frac{1}{28} \). This means that the proportion of failures is \( \frac{1}{28} \). When comparing the two proportions \( \hat{p} \) and \( (1 - \hat{p}) \), we find that \( \hat{p} = \frac{27}{28} \) is greater than \( (1 - \hat{p}) = \frac{1}{28} \). Therefore, the correct inequality is \( \hat{p} > (1 - \hat{p}) \). In summary, the proportion of failures is \( \frac{1}{28} \) and \( \hat{p} > (1 - \hat{p}) \).