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.
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.
1 answer
1 answer