An environmentalist wants to find out the fraction of oil tankers that have spills each month.
Step 2 of 2 : Suppose a sample of 779
tankers is drawn. Of these ships, 600
did not have spills. Using the data, construct the 95%
confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places.
To construct the 95% confidence interval for the population proportion of oil tankers that have spills each month, we can use the formula:
CI = p̂ ± Z*(√(p̂*(1-p̂)/n))
Where:
p̂ = proportion of tankers that had spills = (779-600)/779 = 179/779 = 0.230
Z = Z-score for a 95% confidence interval = 1.96 (from z-table)
n = total number of tankers = 779
Now, plug the values into the formula:
CI = 0.230 ± 1.96*(√(0.230*(1-0.230)/779))
CI = 0.230 ± 1.96*(√(0.230*0.770/779))
CI = 0.230 ± 1.96*(√(0.1771/779))
CI = 0.230 ± 1.96*(√0.000227)
CI = 0.230 ± 1.96*(0.015067)
CI = 0.230 ± 0.02953
Therefore, the 95% confidence interval for the population proportion of oil tankers that have spills each month is approximately 0.200 to 0.259.