According to a study conducted by the California Division of Labor Research and Statistics, roofing is one of the most hazardous occupations. Of 2,514 worker injuries that caused absences for a full workday or shift after the injury, 23% were attributable to falls from high elevations on level surfaces, 21% to falling hand tools or other materials, 19% to overexertion, and 20% to burns or scalds. Assume that the 2,514 injuries can be regarded as a random sample from the population of all roofing injuries in California.
a. Construct a 95% confidence interval for the proportion of all injuries that are due to falls.
b. Construct a 95% confidence interval for the proportion of all injuries that are due to burns or scalds.