You have been provided data on the salaries of a random sample of staff at a large organisation. Complaints have been made that there is unfair pay of the staff who work in section A of the company. The random sample contains salary information, the section they work in (A or B), if they have been promoted recently and what grade they received in the recent performance review (A, B or C).

You are to perform. an investigation into this claim of unfair pay using techniques that have been learned in this course. This includes hypothesis testing and linear models (i.e. everything from weeks 7 to 11 can be used). No outside methods should be used.

Data location: All data is provided on the Moodle in an excel spreadsheet title “Data Assessment 4” .

There are 2 parts to this assessment.

1. Compute the average salary of your sample for section A and B. You should see there is a difference. Use a two-sample Welsh test or a linear model with a factor as a predictor to show that this difference is statistically significant. Whichever method you use is up to you, however all assumptions and the full hypothesis test much be shown. Note, your test should show that there  is a difference. If you believe there is no difference you have made a mistake.

2. Now that you know that there is a difference, if the only significant reason for this difference is the section the staff work in, then that would be an indication of unfair pay. However, there may be a reason that explains this difference that would not be considered unfair. Using hypothesis tests or linear models or whatever else you like from the course, show that either; there  is  no other explanation and therefore the pay is unfair between the sections, or show what you believe to be the factors that led the pay discrepancy.

Tips for part 2: An example of what you may want to do is, consider if there is a difference in pay between people with difference performance levels, and if this difference is statistically significant with a hypothesis test. Or check if there is a difference in promotion rates between section A and B and if this is statistically significant, and soon …

There are multiple ways you can perform. your analysis, so there is not one correct method. You will be awarded partial marks for your attempt even if your final conclusion is not correct so long as your procedure is partially correct and valid and your understanding of the analysis you provided is good.

Important information about your report. Structure

Your report must be structured as a business report. This means it needs references, a conclusion, an executive summary, and the main body. However, as this is a mathematical business report, you need to include your mathematics in the main body as it is part of your argument. Your mathematics must be typeset using the equation editor or similar. You do not need to show all the detail of your working, you only need to show to important calculations, such as hypothesis statements, test statistics, standard error, degrees of freedom, p-values and soon. That is, only the main computation relevant to your argument (your hypothesis tests) in the body. Any working out not relevant to your argument should be placed in an appendix to keep the main body readable, such as data means, variances raw data tables etc. Graphs and tables are important to use where possible as they help the readability to the average person. This is a report to be read by business managers, not by mathematicians. The key part of your writing is to explain the meaning and interpretation of the analysis you have shown.

Excel

You do not need to submit your excel working, however you should place a screenshot of some of your excel in an appendix if you wish to refer to it in your report. You will only submit your report as a word doc or pdf.

Use of AI

The use of AI to help you with understanding is of course proper usage of AI. However the use of procedurally generated text is the assessment is not. You will be heavily penalised for use of AI generated text in your assessment.