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Assignment – Looking at Probabilities & Testing Hypotheses

Overview:

In week 3 you worked with a data set from a rural school system. Specifically, you were provided with standardized test scores for 200 students in Reading and in Math. You will continue to work with that data set and will apply the concepts of probability and hypothesis testing.

Both the quality of your analysis and the quality of your writing will be factored into your grade.

Instructions:

You are, again, writing for your client, the school board. But note that they have made a new hire that allows your discussion to be a bit more formal (see below). You need to address the following topics in a report for the client.

PART 1: UNDERSTANDING THE PROBABILITIES

Help the school system understand the probability of passing tests in math and reading for their students, based on the sample. You need to make clear how you generated the numbers. NOTE: A passing score on the reading and the math test requires a score of 400.

You should consider the group as a whole and also various subgroups of interest to the school system, as those probabilities might not match the probabilities for the sample at large or for other subgroups to which they might be compared.
For example, if I was evaluating my college students, I might wonder if the probability is the same for Freshmen and for Seniors.
You do not need to go beyond the probability concepts discussed in the BASIC PROBABILITY lecture, but you may if you want.
Be sure you show the numbers you used to generate your probabilities, for example,
24 seniors graduated/38 total seniors = .63 or 63% probability of graduating in 4 years.
Organize your content so it is not difficult for your client (and coaches who are grading) to follow.
REMINDER: When working with subgroups, you will have to segment your data set by creating a spreadsheet that has only the observations of interest. For example, I might choose to sort my data and cut and paste the SENIORS to one page and the FRESHMEN to another page in my spreadsheet (using the most simple method to segment). Consider naming your tabs at the bottom so you can keep things straight. There is a video where I showed you how to do this before Project #1.

PART 2: HYPOTHESIS TESTING

Your client is interested in knowing if there is a significant difference between the mean score in math and the mean score in reading. They have no expectation that there is a difference, and if there is a difference, they have no idea which would be larger.

Perform the desired hypothesis test (assuming equal variance and not “pairing” the observations) for your client and explain the results.

Then, use your knowledge to help them learn more, by testing a number of other hypotheses related to test scores. Be clear about what it is that you are testing. As always, you need to discuss what level of confidence you are working with and any assumptions about a directional hypothesis (if you have one).

For example, if I was exploring GPAs for my students, I might want to compare the mean for seniors vs. the mean for freshmen.
If you want to explore paired test (which we mentioned but did not explore), you may, as Excel gives you a menu option for that. Just please do it as an “additional” after you have completed other things in your analysis. Be sure to explain what you are doing and why it might give different results that other tests you ran.

REMINDER: It might be easiest to have data next to each other when making subgroup comparisons (for the easiest to follow method). For example, I might paste my SENIOR’s scores next to my FRESHMEN’s scores so that they are on the same spreadsheet, together.

Audience:

Your audience is your client, the school system.

NOTE: The school system has hired students and she is reasonably well-versed in statistics, so you are speaking to her. As such, you need to be clear about what tests you are running (what hypotheses), what level of confidence, etc. but you can assume that she can follow the statistics. Key takeaways should still be noted so that the report is accessible to others who are not statiticians.

Guidelines:

Your report may be no more than 3 pages. You should think about how to organize your content by learning how to put things next to each other (see video posted in earlier modules). You do not have room for a lot of blank areas in this document.
Submit your report single spaced, with a blank line before and after headings, tables, etc. for readability.
You should use good technical writing techniques:
Have intro and conclusions.
Use headings/subheadings as needed.
Tables, etc. should be titled.
They should not be “orphaned.”
Organization should be thoughtful.
Write in third person and not in first/second (I, we, us).
Tone should be relatively formal, given you are serving as a consultant, but conversational (not too formal or too casual).
Report should be well edited and attractively organized.
Speak to the audience–both the informed and the one that does not know a lot of statistics.
You do NOT need to cite any data source, as the data has been provided to you by the client.
While content will be given more weight, organization and writing quality contribute towards your grade.

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