Whether Outlet Water by Wilson Corporation Has Problems with Nitrates and Ph Levels - Statistics Project Example

Memorandum April 29, Environmental relations manager Statistics group Re: Report on the sampled data This report is based onthe concerns by the State Department of Environmental Services that the outlet water by Wilson Corporation has problems with nitrates and pH levels. This means that the outlet water has quantities that exceed recommended levels. The maximum level for pH is 7.4 while the maximum level for nitrates is 3.0 milligrams per millimeter. The report analyzes and presents findings on temperature, pH, nitrates, phosphates, oxygen, and carbon dioxide in readiness for the hearing that the state department has scheduled for May 2014. Data analysis The following table summarizes the data for the water quantities at the company’s outlet. Table 1: Descriptive statistics for the quantities water temperature pH level Nitrates Phosphates oxygen Carbon Dioxide Mean 15.49474 7.630632 4.545211 0.536695 9.223789 12.06316 Standard Error 0.145313 0.022751 0.201971 0.072906 0.132895 0.567072 Median 15.2 7.6 3.8 0.34 9.4 10 Mode 15 7.6 3 0 9 10 Standard Deviation 1.416332 0.221752 1.968568 0.710604 1.295296 5.527129 Sample Variance 2.005998 0.049174 3.87526 0.504958 1.677792 30.54916 Range 7.98 1 8.685 3.1 9 27 Minimum 11 7.1 0.315 0 3 10 Maximum 18.98 8.1 9 3.1 12 37 The following table shows the confidence interval absolute values as computed from excel, and for the respective water properties. Table 2: Absolute values for intervals Temp pH Nitrates Phosphates Oxygen CO2 0.284741 0.044601 0.395942 0.142974 0.260409 1.111414 Based on the absolute values, confidence intervals, based on excel calculations are shown bellow. Table 3: Confidence intervals for the water properties Temp pH Nitrates Phosphates Oxygen CO2 means 15.49474 7.630632 4.545211 0.536695 9.223789 12.06316 lower limits 15.21 7.58603 4.149268 0.393721 8.96338 10.95174 upper limits 15.77948 7.675233 4.941153 0.679668 9.484199 13.17457 Notice from the state department focuses on pH values and level of nitrates at the company’e outlets but this means possible concerns over other water properties at the company’s outlet. Considering pH values, the mean value for the company’s sampled outlets is 7.631, a value that is considerably higher than the standard upper limit of 7.4. The mode and the median of the sampled outlets are each 7.6 and are above the recommended maximum limit by the state agency. Analysis of the confidence interval for the mean of pH values (7.586, 7.675) also identifies the lower confidence limit to be above the maximum recommended value. This therefore means that the company’s outlet has exceeded to maximum recommended pH value. Consequently, the agency’s position is justified and the company is liable to any penalty that the agency may deem necessary. Even though an observed positive difference exist between the company’s mean pH value and the agency’s recommended value, a test of hypothesis on significance of the difference was necessary. The following set of hypothesis was tested. HO: µ=7.4, There is no significant difference between the mean at the company’s sampled outlets and the agency’s recommended value HA: µ> 7.4; the mean of the sampled outlets is significantly higher than 7.4 The following table summarizes the test of hypothesis results. Table 4: Test of hypothesis results for pH values One-Sample Test Test Value = 7.4 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper ph 10.137 94 .000 .23063 .1855 .2758 The test is significant (t= 10.137, p= 0.000). This means that the observed positive difference between man pH for the company’s sampled outlets and the recommended values is significant. Consequently, the company has no valid statistical ground for disputing the agency’s concern over the high pH levels. Nitrates levels at the company’s outlets is another area of focus in the agency’s concerns and there standards sets 3.0 milliliters as the maximum limit. Data from the company’s sampled outlets however has a mean of 4.545 milliliters for nitrates and this is higher than the agency’s recommended level. Analysis of the 95 percent confidence interval for mean further identifies a higher lower bound, for the mean, than the recommended limit. This therefore suggests that the company’s outlets have higher nitrogen levels than the recommended limit. The observed difference may however not be significant and the following set of hypothesis was conducted to ascertain this. HO: µ=3, There is no significant difference between the mean at the company’s sampled outlets and the agency’s recommended value HA: µ> 3; the mean of the sampled outlets is significantly higher than 3 the following table shows the sample t test results for the test. Table 5: Sample t test results One-Sample Test Test Value = 3 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper nitrates 7.651 94 .000 1.54521 1.1442 1.9462 The test is significant (t= 7.651, p= 0.000). This means that the observed sample mean for level of nitrates is significantly higher that the recommended higher limit. Consequently, the State Department for Environmental Services has substantial grounds to execute penalties on the company for failure to comply with set environmental standards at its outlets. Even though the agency has not raised concerns over the levels of temperature, phosphate, oxygen, and carbon dioxide, obtained results from the two properties can be inferred to the other water properties. This is because the conclusions on pH and nitrates means are based on quantitative data and quantitative data analysis with a large sample size that establishes reliability. The company may therefore lack defense on matters of law and facts at the hearing and moral approach such as an understanding of potential causes of the high values, which do not identify the company’s negligence may therefore be necessary defense. Similarly, the company can develop corrective measures before the hearing and use the measures to assure the agency of its future commitment to environmental standards. The fact that the State Department for Environmental services did not raise concerns over other water properties at the company’s sampled outlets also has an implication that the company could use in it defense at the hearing. It is most likely that the company’s outlets reported good values, values within recommended limits, at the sampled outlets. Though their values may be good, they may have been factors to the high values for nitrates and pH. Establishing a relationship with values of the non contentious properties as the independent variables and those of the contentious properties, pH and nitrates, as dependent variables respectively, could support a position that the noted high values have been hidden under interaction effects of the other variables that are within recommended levels. The following table shows correlation coefficients for the variables. Table 6: Correlation coefficients   temp pH nitrates phosphates oxygen CO2 temp 1 pH 0.554947 1 nitrates 0.317888 0.393231 1 phosphates -0.12167 -0.0493 -0.00523 1 oxygen 0.067373 0.07174 -0.01256 -0.0798 1 CO2 -0.03373 -0.08631 -0.00358 0.067032 -0.2212 1 The correlation coefficients identify negative correlations between nitrates and phosphates, oxygen, and carbon dioxide. A positive correlation is however identified between nitrates and temperature. pH level however has a positive correlation with temperature and oxygen level but a negative correlation with phosphates and carbon dioxide. This suggests that while the company could have made direct efforts to regulate its pH and nitrates levels to recommended values, the properties that are not strictly regulated could be hindering the company’s efforts towards compliance with the agency’s regulations. A regression analysis develops greater insights of potential relationship between both pH level and nitrates level and the other properties explain this. The following table shows regression analysis results for relationship between pH level and phosphates, oxygen, and carbon dioxide levels. Table 7: ANOVA table ANOVA   df SS MS F Significance F Regression 4 1.449184 0.362296 10.2757 6.72E-07 Residual 90 3.173178 0.035258 Total 94 4.622362       The table suggests a significant relationship between pH and the independent variables (F= 10.2757, p= 6.72*107) and the company can argue for shared responsibility with the regulatory body. This is because even though the independent variables are significant determinants of the pH level, regulatory measures do not exist on them, as the agency has not mentioned them. This failure to establish standards over the independent variable is therefore a potential cause for the high pH level. Despite the significance of the independent variables, the analysis of their individual effects on Ph value identifies of temperature only (t=6.288, p= 1.13*108). This further suggests possible interaction effects, and not direct effects, of the independent variables. Table 8: Coefficients for factors to pH   Coefficients Standard Error t Stat P-value Intercept 6.278269 0.262504 23.91686 9.05E-41 phosphate 0.007556 0.027563 0.27414 0.784605 oxygen 0.003783 0.015388 0.245829 0.806374 CO2 -0.00258 0.003598 -0.71758 0.474875 temprature 0.086775 0.013801 6.287556 1.13E-08 Regression analysis for nitrates level also identifies a significant relationship at α= 0.05 as shown below (F=2.259, p= 0.042). Table 9: ANOVA table for nitrates ANOVA   df SS MS F Significance F Regression 4 37.59202 9.398004 2.589121 0.041971 Residual 90 326.6824 3.629805 Total 94 364.2744       Analysis of the individual factors however identifies significance of temperature only (t= 3.2144, p=0.0018).   Coefficients Standard Error t Stat P-value Intercept -2.01593 2.663492 -0.75687 0.451103 X Variable 1 0.087895 0.27967 0.314281 0.754035 X Variable 2 -0.04905 0.156137 -0.31416 0.754127 X Variable 3 -0.00068 0.036507 -0.01876 0.985072 X Variable 4 0.450132 0.140033 3.214476 0.001815 Consequently, hidden factors in the factors that the State Department has not focused on, contributes, indirectly, to the observed high values of pH and nitrates. Conclusion Data analysis shows that the average pH level and average nitrates level in the sampled outlets are significantly higher than recommended maximum values. However, other properties that even the department has not focused on interact to affect values for pH and nitrates. The company should therefore plead guilty to the alleged high values but defend itself against negligence because even the board has also failed to consider the factors that interact to affect the pH and nitrates values. The results also offer a basis for a solution that the company should present during the hearing to show the State Department that it is now able to ensure compliance. Consequently, it should be allowed to operate because it is capable of managing pH and nitrates to recommended levels through management of levels of temperature, pH, nitrates, phosphate, oxygen, and carbon dioxide. Works cited Groebner, David, Shannon, Patrick, Fry, Phillip and Smith, Kent. Business statistics a decision-making approach: Mathxl. Upper Saddle River, NJ: Pearson College Division, 2010. Print. Read More