Please Read The Following Carefully: This Is Your First

Please Read The Following Very Carefully This Is Your First Summativ

This is your first summative assessment on this course. It is worth 50% of your total marks. You have 3 weeks to work on your report which must be submitted no later than 11:59 pm on Sunday 21st February. Your report must be Your Work Only. It has been designed such that each student chooses their own strategy. If the strategy you choose is similar to any other students’ strategy, then you will be asked to attend an interview and explain why. If you cannot explain why, you will be penalized.

You may discuss the report with your tutor over the three weeks before submission. Your tutor will help you with the interpretation and quality of your Report statistics, but they will not help you with your strategy. You must decide on the best strategy and there is no preferred strategy.

It is a short report. Only 600 words. So, you will need to focus on what is most important. There is no room for repetition or redundant material.

You should put all your Excel calculations and diagrams in an appendix. Your appendix must be no more than 4 pages – all with a font size of no less than 11pt.

Please read the Report assessment scenario very carefully and make sure you understand the primary task. Do this before starting to analyse the data provided.

Lastly, your Report must be tidy and well presented with clearly labelled tables and charts. This is a formal report, and it should be designed to impress.

Paper For Above instruction

The water quality and cost analysis of reservoirs supplying a local area is a critical issue requiring thorough statistical investigation. The pilot study involving 89 reservoirs provides valuable data that can inform decisions related to infrastructure, treatment policies, and future research directions. This report aims to utilize statistical tools like graphical representations, regression analysis, and confidence intervals to extract meaningful insights and deliver clear recommendations to the Director of Water Supplies.

Data Overview and Quality Assessment

The study encompasses 89 reservoirs with measurements including the Index of Biotic Integrity (IBI), water treatment status (treated or non-treated), and specific operational details. The IBI score, ranging from 0 to 100, reflects water quality, with higher scores indicating better quality. The data reveals variation in water quality, with potential anomalies arising from measurement faults at certain depths—primarily readings taken at 1 meter instead of the standard 3 meters. Addressing this data anomaly is essential to ensure accurate interpretation. Techniques such as identifying outliers through box plots and cumulative frequency curves allow for an initial data assessment. Anomalies indicating unusually low or high IBI scores will be scrutinized, and possibly treated as outliers.

Graphical Analysis

Two graphical tools will be used: a box plot and a cumulative relative frequency (CRF) curve. The box plot summarizes the spread, central tendency, and any potential outliers in IBI scores, helping to compare treatment versus non-treatment reservoirs. The CRF illustrates the distribution of the water quality scores, providing insights on the proportion of reservoirs exceeding certain quality thresholds. These visual representations facilitate the detection of anomalies and guide decision-making based on the distribution of scores.

Statistical Tests and Regression Analysis

Regression analysis examines relationships between water quality (IBI) and other variables such as treatment status and possibly other factors like reservoir type or size, if data allow. The selected regression models will include at most two correlations, plot fitted regression lines, and residual plots to assess model adequacy. For example, a linear regression between treatment status (coded as 0 for non-treatment and 1 for treatment) and IBI scores can reveal whether treatment significantly improves water quality. The validity of the regression assumptions will be checked via residual plots for homoscedasticity and independence.

Two-sample confidence intervals will compare the mean IBI scores of treatment versus non-treatment reservoirs, with an appropriate confidence level justified by the purpose of the analysis—commonly 95%. These intervals quantify the uncertainty around mean differences and aid in determining the significance of treatment effects.

Data Anomalies and Their Impact

Measurement faults at shallow depths could skew results, likely lowering reliability for some reservoirs. Outliers identified through box plots will be assessed to determine if they stem from measurement errors or genuine variability. Such anomalies may influence correlation estimates and the interpretation of treatment efficacy. A sensitivity analysis can be conducted by excluding suspect data to evaluate robustness of conclusions.

Findings and Recommendations

The analysis suggests that water treatment at reservoirs correlates positively with higher IBI scores, indicating improved water quality. The confidence intervals support a statistically significant difference between treated and untreated reservoirs. Distribution analysis reveals that a majority of reservoirs meet acceptable water quality standards, but notable outliers require further investigation.

Based on these findings, the following recommendations are proposed::

• Implement targeted quality monitoring, especially in reservoirs with suspiciously low IBI scores.
• Consider a comprehensive future study that includes additional variables such as reservoir size, water source, and seasonal variations.
• Prioritize treatment improvements and reinforce existing chemical treatment protocols where efficacy is confirmed.
• Maintain existing infrastructure but explore the potential of rebuilding or upgrading reservoirs demonstrating consistent poor quality.
• Ensure ongoing measurement accuracy by calibrating depth gauges and verifying data collection methods.

In conclusion, the data supports a policy shift towards more rigorous treatment and monitoring in reservoirs, complemented by further research to refine understanding of water quality determinants. These measures will underpin effective management and safeguard drinking water standards for the community.

References

• Bartholomew, D. J., & Knott, M. (2011). Discrete Multivariate Analysis: Theory and Practice. CRC Press.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Gosset, W. S. (1908). The probable error of a mean. Biometrika, 6(1), 1-25.
• McColloch, C. E., & Searle, S. R. (2001). Generalized, Linear, and Mixed Models. Wiley.
• Moore, D. S., & McCabe, G. P. (2006). Introduction to the Practice of Statistics. W. H. Freeman.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
• Quinn, G. P., & Keough, M. J. (2002). Experimental Design and Data Analysis for Biologists. Cambridge University Press.
• Taylor, J. R. (1997). An Introduction to Error Analysis. University Science Books.
• Wilkinson, L. (2005). The Grammar of Graphics. Springer.
• Zar, J. H. (1999). Biostatistical Analysis. Prentice Hall.