The Occupational Safety and Health Administration (OSHA) establishes Permissible Expo- sure Limits (PELs) for nitrous oxide of 50 ppm. Measurements from a chemical plant yielded the following ppm values for nitrous oxide: {48, 42, 58, 45, 51, 39, 45, 58, 43, 50, 43, 43} You can assume that the true distribution is Gaussian. (a) State the null and alternative hypotheses for a test meant to show that the plant violates the standard. (b) Which statistic is appropriate for this test and what is its distribution? (c) Compute the p-value for the test statistic. (d) Can we conclude to a 5% significance level that the plant violates the standard?