An environmentalist wants to find out the fraction of oil tankers that have spills each month. Step 2 of 2 : Suppose a sample of 281 tankers is drawn. Of these ships, 228 did not have spills. Using the data, construct the $90 \%$ confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places. Answer How to enter your answer (opens in new window) Lower endpoint: Upper endpoint:

Step 1 ：Given that a sample of 281 tankers is drawn and 228 of these ships did not have spills, we are to construct the $90 \%$ confidence interval for the population proportion of oil tankers that have spills each month.

Step 2 ：First, we calculate the sample proportion $\hat{p}$, which is the number of successes (tankers that did not have spills) divided by the sample size. In this case, $\hat{p} = \frac{228}{281} = 0.811$.

Step 3 ：The Z-score for a $90\%$ confidence level is approximately 1.645.

Step 4 ：The formula for a confidence interval for a proportion is given by $\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $Z$ is the Z-score corresponding to the desired confidence level, and $n$ is the sample size.

Step 5 ：Substituting the values into the formula, we get the lower and upper endpoints of the confidence interval as $0.773$ and $0.850$ respectively.

Step 6 ：\(\boxed{\text{Final Answer: The } 90 \% \text{ confidence interval for the population proportion of oil tankers that have spills each month is approximately } [0.773, 0.850].}\)