The Deepwater Horizon oil drilling platform exploded on April 20, 2010, killing 11 workers and causing the largest oil spill in American history. Many Americans participated in the cleanup of coastal property and wildlife habitat, including the cleaning of the wildlife. The National Institute for Occupational Safety and Health (NIOSH) conducted a randomly sampled survey of 54 of these workers who were exposed to oil, dispersant, cleaners, and other chemicals. Of these 54 workers, 25 reported skin problems, such as itchy skin or rash, as a result of exposure to these chemicals. We are interested in constructing a 95% confidence interval for the population proportion of all wildlife workers who reported such skin problems.
What is the point estimate of the population proportion of workers reporting skin problems?
What are the conditions required for constructing the desired confidence interval?
What is the critical value Z_(a⁄2)?
Calculate and interpret the margin of error.
Calculate and interpret the 95% confidence interval for the unknown population proportion of workers reporting skin problems.
How large sample size would be needed to estimate the population proportion of all wildlife workers who reported such skin problems with a MOE of 0.1330 and 95% confidence? Comment on your answer.
Suppose we now want the estimate to be within 0.1330 with 99% confidence rather than 95%. Will the required sample size be larger or smaller and why? Verify your statement by finding the required sample size.
Test the hypothesis that me population proportion of workers reporting skin problems is not equal to 0.61 at the 0.05 significance level. State the null hypothesis and the alternative hypothesis. Calculate the p-value. Is your p-value consistent with your confidence interval from (e)? Explain.