Homework answers / question archive / I have a data set of 100 NBA players and it is my job to discover whether 80% of the players with productivity levels above the median level are married ECON1203   Business       and Economic        Statistics       TERM    3,     2020      Case       Study:    The Marriage        Premium      MILESTONE 2        In the first milestone of this case study, you had the opportunity to know your dataset and to understand some of the key characteristics of the players, their demographics and income

I have a data set of 100 NBA players and it is my job to discover whether 80% of the players with productivity levels above the median level are married ECON1203   Business       and Economic        Statistics       TERM    3,     2020      Case       Study:    The Marriage        Premium      MILESTONE 2        In the first milestone of this case study, you had the opportunity to know your dataset and to understand some of the key characteristics of the players, their demographics and income

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I have a data set of 100 NBA players and it is my job to discover whether 80% of the players with productivity levels above the median level are married

ECON1203   Business       and Economic        Statistics      

TERM    3,     2020     

Case       Study:    The Marriage        Premium     

MILESTONE 2     

 

In the first milestone of this case study, you had the opportunity to know your dataset and to understand some of the key characteristics of the players, their demographics and income.   

 

In your second meeting with the EqRA senior consultant, Dr. Rachel Ng, discussed with you the objective of commissioning this study. The Board members would like to understand the dynamics between marriage and income. Keep in mind that the premium is being measured as a gain over players of similar demographics, career stage and ability.

 

 

Task 1:

To further understand the dynamics between wages and the players’ demographics, Dr. Ng asks you to test your data against the following claims 

 

1. Marriage & Age. The marriage premium has the greatest impact on younger players and high performers and weak-to-no impact on older players.  

 

2. Marriage & Race. The marriage premium is a racial phenomenon impacting on the wages of the black players only.

 

3. Marriage & Productivity. There is no correlation between marriage and productivity, except for low performers who see a jump in performance after marriage. (Here you may use the Productivity Index as a measure performance). You may choose to define ‘low performers’ those in the bottom first quartile of the distribution of performance.

 

4. Marriage & High achievers. At least 80% of the players with productivity above the median level (as measured with the Productivity Index) are marrie

 

Task 2:

Anxious to get a quick answer, Dr. Ng asks that you simply test the claim of a marriage premium by testing a null hypothesis of zero difference in the average wages between married and unmarried players. Use simple linear regression to test this claim. Report the result and explain to Dr. Ng why this is not a good idea.

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As part of your reporting requirements please state your assumptions. Remember to show all your working.

Please write a short report on the results of any hypothesis tests performed and the interval estimates of the parameters. As part of your report you’ll need to explain why and potential issues with this dataset and possible remedies for any issues that may arise. 

Keep in mind that this is a kind of a research exercise where you are dealing with real dataset. There is no correct or wrong answer. BUT there is incorrect use of statistical techniques and assumptions. Or worse, incorrect interpretation of the results and misleading the Board! The latter is what we want to learn to avoid. 

Data

Please refer to the Milestone 1 document. 

Hints

You may (if necessary) want to use a simplifying assumption of normality or use the CLT. A useful statistical result is that the sum and difference of two normal random variables is a normal random variable. 

You may assume independence when necessary (for example between the distribution of income of singles and that of married players!)

You may separate players into groups (along side age, performance and marital status) to test the above claims (of differences between groups).

 

 

 

 

 

 

Guidelines for Milestone 2 report 

For this Milestone 2 report there are seven main areas we will be looking for:

Introduction: which summarises what the purpose of this report and highlights how this report is going to be structured. Remember to provide some background information about the topic.

Hypothesis testing: Have you correctly defined the null and alternative hypothesis, the decision rule, calculated the test statistics and concluded the test.

Confidence intervals: Have you construct the intervals correctly, used the correct distribution and make the correct conclusion?

Analysis and contents: Have you analysed and concluded correctly for each of the tests and confidence intervals? Have you been able to say something about how representative your sample is? Is it appropriate in the context of your results and what can you say on this front? In other words do you have a coherent content as well when you're weaving your results together?

Assumptions: Have you stated all the assumptions that are appropriate for your conclusions/tests.

Limitations: What are the limitations of your results?

Conclusions: which should summarise the findings of your investigation and any concluding comments.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Administrative Details

Length:         Total length should not exceed 1500 words (not including tables and graphs) and 10 pages (including table, graphs and appendices). Please use 10pts to 12pts fonts. Your mark will be based on the first 1500 words and first 10 pages. The rest will not be marked!

As a style guide, you may put some or all the tables/graphs as an appendix and refer to them in your report as necessary.  Include only graphics/tables to substantiate your analysis/conclusions and findings. In the process of preparing your work, you will go through many tables and graphs, which are most probably not relevant for Dr. Ng to see. So be very selective and make good use of the pages limit! As a general guide, labels (including graphs, labels of axis), and any captions, footnotes, titles, tables, any headers and footers are included in your page limit but not in the word count. 

Report mark:	The report will be marked out of 12.5 and will constitute 12.5% of your total mark for the course. There is a 2.5% allocated to Peer and Self Review Task for Milestone 2.
Due date:	You must submit only one electronic copy for both you and your teammates to the course Moodle site by 23:55 (11:55 PM) of 13/11/2020 (Friday, WEEK 9).
Late submissio n:	20% of the value of the project will be deducted for every day or part thereof that the hard copy is turned in after the deadline (including the weekend). Projects submitted more than five days late will not be marked and will be assigned a mark of zero. You and your teammates should be working on the material regularly before the due date. Extensions will only be granted in exceptional circumstances and must be approved by the lecturer-in-charge.  For more details about late submission, see the Course Outline.
Plagia- rism:	Evidence of plagiarism will be treated extremely seriously: automatic and immediate failure in the course is a possible

penalty. See Part B of the course outline for further details about UNSW’s policies on plagiarism. If you are in doubt about how to identify or avoid plagiarism, follow the link to and complete the self-paced Working with Academic Integrity module on Moodle.

 

Coverage: In this milestone, you are only expected to use the statistical techniques developed in the text and lectures up until the end of WEEK 8.

 

At last Please do enjoy and have fun uncovering the information that lay behind the data in your hands. Don’t be afraid to be critical and to think outside the box.