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**Assessment 4: **Report** Word limit: **1500 (+/- 10%; not including Appendix or Executive Summary)** Weighting: **15%** Due date: **9am AEST Monday, 28 September (Week 12)

**Assessment overview:**

For this assessment, you need to produce a report by generating responses to six tasks presented below. For some of these sections, you will need to use Excel to generate statistical output (statistical analyses and graphs). The report should be presented in the form of a business report to a senior manager who cannot be assumed to have any particular knowledge of statistical methods. Microsoft Word and Excel should be used to complete this assessment. Your statistical calculations should be carried out using Excel only.

**Assessment details**

You will need to download the Excel dataset ‘bankdata.xls’ from Blackboard. The data set is about banking, and is supplied by the ‘*Ordinary People’s Bank*’. There are 1000 cases in this data set, and six variables as follows:

- TYPE: Type of account (C:Cheque, S:Savings and V:Visa)

- SEX: Gender (F:Females and M:Males)

- AGE: Age of the account holder in years

- BALANCE: Account balance

- OPEN: Account open (1:Open and 0:Not Open)

- TRANSACTIONS: Total transaction in whole dollars

You will use this data set to generate responses to the following six tasks.

**Select a random sample**

Select a random sample of size 50 from the given 1000 cases in the banking data set. You will use this sample data to complete tasks 2 to 6.

**Descriptive statistics**

Use data summary methods to describe the insurance policy holders in your sample using the six variables. Use an *appropriate* graphical and summary statistical technique, chosen according to the type of variable (note that less appropriate/inappropriate techniques will receive fewer/no marks). Choose your techniques from:

**Tabular Techniques**: frequency tables and grouped frequency tables.

**Graphical Techniques**: pie chart, bar graph, histogram, frequency polygon.

**Summary Statistics**: mode, median, mean, standard deviation, range, coefficient of variation and interquartile range.

**Do not draw an ogive curve, stem plot, or a box plot in this assignment and do not draw 3-D graphs.**

- For a nominal or an ordinal variable draw a graph and present a frequency table in percentages.

- For a ratio or an interval variable draw a graph and a summary statistics table, including summary statistics appropriate to the type of distribution only.

- Try to use variation in drawing graphs e.g. pie chart/bar chart or histogram/polygon.

- Do not draw two different graphs for the same variable. You can draw the same type of graph for two variables.

- Do not include any information that you will not include in your discussion such as kurtosis.

- Display and describe one variable at a time.

**Confidence intervals**

Estimate the following quantities, using 95% confidence intervals. Explain the meaning of your confidence intervals.

- The average age of account holders for
**the open accounts only.**

- The average total transaction dollars for all accounts. Compare both intervals with their respective true means by calculating the actual population mean for the full 1000 cases, and comparing the population mean to the sample mean and confidence interval (note: it is not usual to do this, so you are asked to do this for the purpose of this assignment).

Your confidence interval should start with ‘We are 95% confident that…”. This section should take half a page or less.

NB: Please make sure you provide sufficient information in the appendix for your confidence interval calculations to be replicated, so they can be checked.

**Hypothesis testing**

- It is often felt that female account holders have different account balances on average than male account holders.
**For this hypothesis only consider open accounts**. Investigate this contention by carrying out an appropriate hypothesis test.

- It is often felt that the average transaction dollars differ for Visa and non-visa accounts.
**Use account****type for this test**.

Only report a **non-technical** explanation of your methodology and your findings in the main section of the report. The computations **and output should be placed in an appendix, including the test statistic, p-value and degrees of freedom. This should take half a page or less.**

**Correlation and regression**

In this section you will investigate the relationship between the transaction dollars and age of the account holders for open accounts only. Using these two variables (transaction and age) develop a regression model to predict average transaction dollar from age. Make sure that you undertake a full regression analysis, *with appropriate discussion* and include:

- a scattergram and a brief discussion

- an estimate of the linear regression model

- the coefficients of correlation and determination

- a test of the hypothesis that there is no linear relationship between transaction dollars and the age of an account holder.

Ensure your scattergram includes a line of best fit. Also, make sure you describe the relationship between the variables using R and R-square, and interpret the slope, coefficients and the results of the hypothesis test.

**Conclusion**

Provide a brief, concise summary of all of your findings and briefly mention any limitations in your findings. Make sure you do not give tables or graphs here.

The report should be presented in the form of a business report to a senior manager who cannot be assumed to have any particular knowledge of statistical methods.

Make your report informative but concise and use a non -technical style. Do not just quote statistics or analysis results but explain what they mean. In general, **do not include in the report** formulae, calculations, definitions of statistical terms or discussions on how graphs are constructed. Where appropriate these may be included in the appendices.

It is **important** that the values which have been calculated are correctly **analysed, discussed and** **interpreted**, and that a** written description **of the main features of the tables and graphs that have been constructed is included. The emphasis in this assignment is on **interpretation and analysis**, not just the computation of statistics and construction of graphs. It will be assumed that all computations have been correctly performed and that graphs have been properly constructed. Nevertheless, marks will be deducted if these are inaccurate or incorrect.

Presentation is an important feature of a business report. The guide to presentation that follows gives a general outline to report writing.

**Executive Summary**

- Report only the highlights of the findings.

- Entice an Executive to read on.

- Essentially a lively summary of the main conclusions.

- No longer than one page
**; this is not counted in the word count**and must be on a separate page from the rest of the report.

**Introduction**

- State the purpose of the report i.e. what you will discuss in the report

- Outline the contents of the Report

- Provide a brief description of the methodology

- Describe the source of the data and state its location in the report.

- This should contain information about what we expect to read in the project.
**This should take about****half a page.**

**Analysis**

- Contains a thorough yet
**non-technical**description of all the findings (graphs and tables will be included only where they help this discussion). - Details the results that were highlighted in the Executive Summary

**Do not include any calculations here**but include appropriate graphs and tables which are needed to support your discussions.

**Conclusion**

- Report the findings and results of your work.

- Essentially an expansion of the executive summary written from the point of view that the Executive Summary has not been read.
- End with a discussion of the limitations of your analysis (e.g. reference to sample size if small, or comment on the data if it is old).

**Appendices**

- Must be referred to in the main body of the report.

**Must contain your selection of random numbers and related random data.**

- Include the raw data, charts and tables that are
**not essential**, but support the ANALYSIS section.

- Include your EXCEL output for descriptive statistics, confidence intervals, hypothesis testing and regression.

- Include any other relevant calculations.

**Please make sure the information in the appendix is sufficient for all calculations to be replicated**, so they can be checked e.g. if you include output for your confidence intervals, please show how this output was used to calculate the confidence intervals.

Graphs must be in the Main body along with relevant tables and discussion. **Graphs kept only in the** **appendices will not score any marks for graphs.**

Keep the appendices to a moderate size. Marks are only given for the report itself. Your Excel work confirmation will be checked in the Appendices. The emphasis in this assignment is on interpretation and analysis, not just the computation of statistics and construction of graphs. Make your report informative but concise and use a non-technical style. Do not just quote statistics or results of analyses but explain what they mean. In general, do not include formulae, calculations, definitions of statistical terms, or discussions on how graphs are constructed. Where appropriate these may be included in the appendices.

**Assessment criteria**

Marks for this assessment are broken down as follows:

**Presentation 8%**- include cover page, avoid technical language, within 1500 word limit (excluding executive summary and appendix), minimal spelling, grammatical or syntactical errors, clear expression, clear tables/graphs, information is provided in the correct section, includes introduction and conclusion.

**Executive summary 8%**- includes main findings/highlights only, well written, entices the reader to read on.

**Introduction 4%**- summarises the source of the data, the aim of the report, the variables to be examined, and the processes used.

**Descriptive statistics 24%**- appropriate graphical and summary statistics according to the type of variable, and the type of distribution.

**Confidence intervals 12%**- correct calculation and expression, and includes comparison to population mean.

**Hypothesis tests 12%**- correct calculation, analysis and correct interpretation.

**Correlation and regression 16%**- correct scattergram; presents and interprets correlation coefficient, coefficient of determination, regression equation and hypothesis test.

**Conclusion and limitations 8%**- all findings summarised, limitation(s) discussed, well expressed and well structured

**Appendix with Excel outputs 8%**- includes all cases in random sample, output showing creation of classes for graphs (where relevant), output and calculations for confidence intervals and hypothesis tests, output for regression analysis; output is sufficient for calculations to be replicated thereby allowing the results to be checked.

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