To calculate the confidence interval, we first need to find the sample proportion of tankers that had spills.
Sample proportion (p̂) = Number of tankers with spills / Total number of tankers
= (356 - 253)/356
= 103/356
≈ 0.289
Next, we need to calculate the margin of error:
Margin of error (E) = Z * √(p̂ * (1 - p̂) / n)
= 1.645 * √(0.289 * 0.711 / 356)
≈ 0.037
Finally, we can construct the 90% confidence interval:
Confidence interval = p̂ ± E
= 0.289 ± 0.037
= (0.252, 0.326)
Therefore, the 90% confidence interval for the population proportion of oil tankers that have spills each month is approximately (0.252, 0.326).
An environmentalist wants to find out the fraction of oil tankers that have spills each month.
Step 2 of 2 : Suppose a sample of 356
tankers is drawn. Of these ships, 253
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.
1 answer