**Educational Website: Statistical Analysis of Arsenic Levels in Groundwater****Introduction:**Arsenic is found naturally in some groundwater sources. A mean arsenic level of 8.0 parts per billion (ppb) is deemed safe for agricultural use. In this scenario, a Texas well used for watering cotton crops is tested for arsenic using a sample of 36 tests yielding a mean of 7.0 ppb with a standard deviation of 2.3 ppb. We are tasked with determining if the arsenic level in the well is less than 8.0 ppb using a significance level of 0.01.**Questions and Calculation:**(a) **What is the level of significance?**- \(\alpha = 0.01\).(b) **State the null and alternate hypotheses.**- \(\text{H}_0: \mu = 8 \text{ ppb}; \text{H}_\text{a}: \mu < 8 \text{ ppb}\).- (Choose the appropriate set from options provided.)(c) **What sampling distribution will you use? Explain the rationale for your choice.**- Use the standard normal distribution since the sample size is large (\(n = 36\)) and the standard deviation is known.(d) **What is the value of the sample test statistic? (Round your answer to three decimal places.)**(e) **Find the P-value. (Round your answer to four decimal places.)****Graphical Representation:**- **Top Graph:** Displays a normal distribution curve centered at 0, with a shaded region in the left tail representing the area corresponding to the calculated P-value. - **Bottom Left Graph:** Similar curve but illustrates further into the left tail area.- **Bottom Right Graphs:** Additional normal distribution curves emphasizing tail areas.(f) **Based on your answers in parts (c) to (e), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \(\alpha\)?**- If P-value \(\leq \alpha\), reject \(\text{H}_0\), indicating statistical significance at \( \alpha = 0.01 \).(g) **Interpret your conclusion in the context of the application.**- If sufficient evidence at 0.01 level, the mean arsenic level is less than 8 ppb.- If insufficient evidence,

nfortunately, arsenic occurs naturally in some ground watert. A mean arsenic level of -8.0 parts per bilion (pob) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of7.0 pob arsenic, with s-2.3 pob. Does this information indicate that the mean level of arsenic in this well ess than ppb Use 0.01. Ca) What s the level of significance State the nul and aternate hypotheses OM pob, pp OMi> ppb; pob OM popb; ppb OMi ppb; ppb OMo! pob pob () what sampling distribution wil you use? Explain the rationale for your choice of sampling distribution. O The standard nermal, since the sample sieis large and eis unknown O The Student's e since the sample size is large and e is unknown. O The standard normal, since the sample size is large and e is known. O The Student'st, since the sample size is large and e is known. What is the value of the sample test statistic (Round your answer to three decimal places.) (e) Find the Avalue. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the Pvalue (4) Based on your answers in parts (a) to (c), will you reject or fall to reject the nul hypothesis? Are the data statistically significant at level a O At the a0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O AL the a0.01 level, we fal to reject the nul hypothesis and conclude the data are statistically significant O At the e0.01 level, we fal to reject the nu hypothesis and condude the data are not statisticaly significant. (e) Interpret your conclusion in the context of the application O There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than ppb. O There is insuficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than ppb.