Environmental engineers are using data collected by weather data centers to learn how climate affects the sea ice. Of 518 ice melt ponds studied in a certain region, 79 were classified as having "first-year ice". The researchers estimated that about $15 \%$ of melt ponds in the region have first-year ice. Estimate, with $90 \%$ confidence, the percentage of all ice-melt ponds in the region that have first-year ice. Give a practical interpretation of the results. Construct a $90 \%$ confidence interval around the sample proportion of ice melt ponds with first-year ice. (Round to four decimal places as needed)

Step 1 ：First, we need to calculate the sample proportion (p̂) of ice melt ponds with first-year ice. This is given by the number of successes (first-year ice ponds) divided by the total number of trials (total ponds studied). So, \(p̂ = \frac{79}{518} = 0.1525\).

Step 2 ：Next, we calculate the standard error (SE) of the sample proportion. The standard error is given by the formula \(SE = \sqrt{\frac{p̂(1-p̂)}{n}}\), where n is the total number of trials. Substituting the values we have, \(SE = \sqrt{\frac{0.1525(1-0.1525)}{518}} = 0.0174\).

Step 3 ：Since we are asked to construct a 90% confidence interval, the critical value (z*) corresponding to this confidence level is 1.645 (you can find this value in a standard normal distribution table).

Step 4 ：Now, we can calculate the margin of error (ME) for the confidence interval. The margin of error is given by the formula \(ME = z*SE\). Substituting the values we have, \(ME = 1.645*0.0174 = 0.0286\).

Step 5 ：Finally, we can construct the 90% confidence interval for the population proportion (p) of ice melt ponds with first-year ice. The confidence interval is given by the formula \(CI = p̂ \pm ME\). Substituting the values we have, \(CI = 0.1525 \pm 0.0286\). So, the 90% confidence interval is \(\boxed{(0.1239, 0.1811)}\).

Step 6 ：The practical interpretation of this result is that we are 90% confident that the true proportion of all ice-melt ponds in the region that have first-year ice is between 12.39% and 18.11%.