One of the major sources of sulfur dioxide air pollution is coal powered utility plants. In 2010, only 20% of coal powered utilities met EPA air pollution standards. Several major changes were made in the power plants in 2011, such as using low-sulfur coal, burning the coal at a higher temperature, and installing new scrubbers on the air stacks of the plants. In 2019, the EPA randomly selected 25 power plants for an evaluation of their air pollution. The investigators found that 8 of the 25 power plants met the EPA air pollution standards, whereas 17 power plants failed to meet the standards. 1. Is there significant evidence at the = .05 level that the proportion of power plants meeting the EPA air pollution standards in 2019 has increased from the 20% meeting the standards in 2010? 2. Compute the P-value for the value for the test in part 1.

3. What is the probability that the test from part 1 will detect that the proportion of power plants meeting the EPA air standards increased to 30% in 2019?

4. Place a 95% confidence interval on the proportion of coal powered utility plants meeting the EPA standards in 2019.

5. The researchers are interested obtaining a very accurate estimate of the proportion of power plants meeting the standard in a new study. How large must the sample size n be in order that the researchers can be 95% confident that the sample estimator of the proportion meeting the standard is within .05 of the true value?