Giving a test to a group of students, the grades and gender are summarized below \begin{tabular}{|r|r|r|r|r|} \hline & A & B & C & Total \\ \hline Male & 20 & 7 & 16 & 43 \\ \hline Female & 8 & 15 & 18 & 41 \\ \hline Total & 28 & 22 & 34 & 84 \\ \hline \end{tabular} Let $p$ represent the proporton of all male students who would receive a grade of B on this test. Use a $96 \%$ confidence interval to estimate $p$ to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents). State the point estimate for the proportion of all male students who would receive a grade of $B$ on this test: $p \approx$ State the margin of error for the proportion of all male students who would receive a grade of $B$ on this test: $\mathrm{EBP} \approx$ Question Help: $\square$ Video $\square$ Message instructor

Step 1 ：Calculate the point estimate for the proportion of all male students who would receive a grade of B on this test. This is done by dividing the number of male students who received a grade of B by the total number of male students. In this case, it is \(\frac{7}{43} \approx 0.163\).

Step 2 ：Calculate the standard error of the proportion using the formula \(\sqrt{\frac{p(1-p)}{n}}\), where \(p\) is the point estimate of the proportion and \(n\) is the total number of observations. In this case, it is \(\sqrt{\frac{0.163(1-0.163)}{43}} \approx 0.056\).

Step 3 ：Calculate the margin of error for the proportion of all male students who would receive a grade of B on this test using the formula \(Z*\sqrt{\frac{p(1-p)}{n}}\), where \(Z\) is the Z-score corresponding to the desired level of confidence (in this case, 96%), \(p\) is the point estimate of the proportion, and \(n\) is the total number of observations. In this case, it is \(2.054*\sqrt{\frac{0.163(1-0.163)}{43}} \approx 0.116\).

Step 4 ：The 96% confidence interval for the proportion of all male students who would receive a grade of B on this test is \(p \pm EBP\), or equivalently, \(0.163 \pm 0.116\), which simplifies to \(0.047 \leq p \leq 0.279\).

Step 5 ：\(\boxed{0.047 \leq p \leq 0.279}\) is the final answer.