We have the following situation:
• We have a sample of 1453, n = 1453.
• Of these ships, 989 did not have spills.
And from this, we need to estimate the proportion of oil tankers that had spills.
To find it, we can proceed as follows:
1. We need to find the sample proportion of ships that had spills. These ships are:
[tex]\begin{gathered} 989\text{ ships did not have spills from 1453.} \\ \text{ Then the ships that have spills are:} \\ 1453-989=464 \end{gathered}[/tex]
2. Then the sample proportion is given by:
[tex]\begin{gathered} \hat{p}=\frac{464}{1453}=0.319339298004 \\ \\ \text{ If we round this value to a decimal number rounded to three decimal places: } \\ \\ \hat{p}=0.319 \end{gathered}[/tex]
Therefore, in summary, the proportion of oil tankers that had spills is (as a fraction or decimal with three places):
[tex]\begin{gathered} \hat{p}=\frac{464}{1453} \\ \\ \hat{p}=0.319 \end{gathered}[/tex]
