### Environmental Protection Agency Standards AnalysisThe Environmental Protection Agency (EPA) mandates that the concentration of lead in drinking water must be below 15 parts per billion (ppb). A study involving twelve water samples from a specific source resulted in the following lead concentrations, measured in ppb:- **Sample Concentrations**: - 11.4, 13.9, 11.2, 14.5, 15.2, 8.1 - 12.4, 8.6, 10.5, 17.1, 9.8, 15.9 ### Hypothesis TestingA hypothesis test will be conducted to ascertain if the water from this source complies with the EPA standard. The process involves the following steps:#### a. Null and Alternate Hypotheses- **Null Hypothesis (H₀)**: The mean lead concentration in the water is 15 ppb or higher.- **Alternate Hypothesis (H₁)**: The mean lead concentration in the water is less than 15 ppb.#### b. P-value Computation- Calculate the P-value to determine the probability of observing the sampled data, assuming that the null hypothesis is true.#### c. Conclusion- Based on the P-value, assess whether there is sufficient evidence to conclude that the water meets the EPA standard. Provide a detailed explanation of the decision-making process. This testing is critical to ensure compliance with safety standards and protect public health.

From the provided information, Sample size (n) = 12 The EPA standard require that the amount of lead in drinking water be less than 15 ppb.a) The hypotheses for this test can be constructed as: Null hypothesis H0: µ = 15 Alternative hypothesis H1: µ < 15The mean and standard deviation of data can be obtained as: x=∑xn=11.4+⋯+15.912=12.383s=∑x-x2n-1=11.4-12.3832+⋯+15.9-12.383212-1=2.932The value of test statistic can be obtained as: t=x-μsn=12.383-152.93212=-3.09 The test statistic is -3.09.Degrees of freedom = n - 1 = 12 - 1 = 11 b) The p value of test statistic can be obtained using excel function as: =T.DIST.RT(3.09,11) The excel output is as follow: The p value is 0.005143. c) Since, the p value is less than level of significance (0.05), therefore, the null hypothesis would reject and it can be concluded that there is sufficient evidence to support the claim that the mean amount of lead in drinking water is less than 15 ppb. Yes, we can conclude that the water from this source meets EPA standard.