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This task requires you to deal with single and joint discrete probability distributions, the calculations of probabilities

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Portfolio Assessment

Introduction

The first coursework assignment for this module is a group portfolio of short tasks worth a cumulative 50% of the overall module mark. You are asked to complete five tasks for the portfolio. All five tasks are based on real world data and require you to produce statistical analysis based on the concepts and theories we are learning throughout the term. We have now gone through enough material in the module so far, for you to be able to start working on the portfolio straightaway. There are still some topics that we will cover in the second part of the term and that will be needed for you to complete the portfolio. However, I would suggest that you get started with the portfolio and you work through the tasks over the coming weeks. For example, you could already complete tasks 1 and 2 (and possibly 3) and the remaining three over the following weeks. Do not leave the work until the last moment. Your overall performance is likely to greatly benefit from working regularly throughout the term. The portfolio should be submitted by 8th April 2022, 4pm (London time).

Group or Individual Work

The portfolio assessment can be completed either as a group work or you can work on your own. I have a preference for you to work in a group because sharing ideas, thoughts, views, opinions helps to make your work richer and more creative. If you set up a group, I would like the group to include no more than three/four people and my expectation is that you will work together on the five tasks by actively collaborating, sharing the work and consulting each other on a regular basis. Each group should appoint a ‘group leader’ who will keep in regular contact with me and the class teachers and will inform us of the group progress. Any concern about the group’s ability to work together should be communicated as soon as possible to me or the class teachers. Whether you decide to work with a group or on your own, please record your group names or just your individual name and ID on this online spreadsheet by 30th March 2022 (the link is also available on Moodle):

EC1011 Portfolio Groups & Individuals.xlsx

 

 

Introduction to the Portfolio Tasks

The portfolio is made up of five tasks that ask you to engage with some real world data drawn from the UK survey called ‘Opinions and Lifestyle Survey’. This survey is carried out monthly by the Office for National Statistics (ONS) and the data used for this portfolio refers to the period April – May 2015. The dataset is available on Moodle and is named “EC1011 Portfolio Dataset.xlsx”.

 

A Brief Introduction about the Lifestyle Survey

The Opinions and Lifestyle Survey is a multipurpose social survey which provides quick and reliable information about topics of immediate interest. The survey has a monthly cycle and specialises in asking pertinent research questions on topics too brief to warrant full surveys of their own. Government organisations, academic institutions and charities can commission questions on the ONS Opinions Survey and use the survey in a variety of different ways. This is mostly to provide answers to questions of immediate policy interest but also to help assess public awareness of new policies, initiatives and publicity campaigns; to develop, test and pilot new survey

questions; or to obtain samples of respondents for follow‐up research projects.

 

Main Topics

Each month's questionnaire consists of two elements: core questions, covering demographic information, are asked each month together with non-core questions that vary from month to month.

The non-core questions for the April – May 2015 months were regarding Well-Being (Module MCZ): this module was asked on behalf of ONS and all questions ask respondents to rate their feelings towards different aspects of their lives, generally using a scale of 0-10, where 0 is generally low and 10 high. You can find a list of the variables and their description in the appendix at the end of this document (page 7).

 

Coursework Brief

The portfolio is made up of five tasks. Please complete each task in separate worksheets in the same file that contains the dataset. Label each worksheet with the number of the task i.e. Task 1, Task 2 etc. It is important that for each question there is clear evidence of how the answer has been calculated i.e. there should be formulae, functions, explanations etc. that show how the solution has been computed. The comments should be typed in ‘text boxes’ inside the Excel document. Formulae/functions/graphs/tables do not count towards the word limit.

Task 1

This task requires you to deal with single and joint discrete probability distributions, the calculations of probabilities, functions of random variables and types of distributions. Complete this task in a worksheet labelled ‘Task 1’ and clearly show your solutions and, where required, add your comments. The comments should not exceed the 400 words limit. Task 1 accounts for 20 marks.

Task 2

This task requires you to engage with the insights of the Central Limit Theorem. Complete this task in a worksheet labelled ‘Task 2’ and clearly show your solutions and, where required, add your comments. The comments should not exceed the 200 words limit. Task 2 accounts for 20 marks.

Task 3

This task asks you to engage with point estimation and, in particular, to compute and compare two Point Estimators. Complete this task in a worksheet labelled ‘Task 3’ and clearly show your solutions and, where required, add your comments that should not exceed the 200 words limit. Task 3 accounts for 20 marks.

Task 4

This task asks you to engage with inferential statistics for the population mean with a particular focus on hypotheses concerning the level of ‘happiness’ across individuals who are in different employment status. Complete this task in a worksheet labelled ‘Task 4’ and clearly show your solutions and, where required, add your comments that should not exceed the 300 words limit. Task 4 accounts for 20 marks.

Task 5

This task asks you to engage with inferential statistics for the population proportion with a particular focus on hypotheses concerning the proportion of individuals with a ‘degree or equivalent’ level of education. The task also asks you to investigate differences in the proportion of women and men with a ‘degree or equivalent’ qualification. Complete this task in a worksheet labelled ‘Task 5’ and clearly show your solutions and, where required, add your comments that should not exceed the 300 words limit. Task 5 accounts for 20 marks

Feedback

We will be happy to provide you with some feedback on one of the portfolio tasks during the term provided that any request reaches us by 30th March at the latest.

Submission Deadline

You are expected to submit one excel file that contains six worksheets: one worksheet with the actual data and one for each of the five tasks. Each worksheet should contain details of the solutions and comments wherever needed.

The portfolio coursework has one single submission point which is Friday 8th March 2022, 4pm (London time).

 

Task 1

 

1) Use the Excel functions to compute the average, median, mode, minimum, maximum, variance and standard deviation of the variable MCZ_1. Briefly comment on your findings.

2) The variable MCZ_1 measures the overall satisfaction of each respondent to the survey and we could regard it as a sort of measure of ‘happiness’. Produce a relative frequency distribution of ‘happiness’ and plot an appropriate graph displaying the distribution.

3) Use the relative frequency distribution to:

a. Compute the expected rating. Comment on and interpret your findings.

b. Compute the variance and the standard deviation of rating. Do you get values similar to the ones you computed in 1)? Briefly comment on your findings.

 

 

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