Paper 1: STA 2183W
Initial Draft Due September 30th at 11:59PM.

The Internal Revenue Service (IRS) claims that three of its forms (Form A, B, and C) should each
typically take about 160 minutes to fill out. A researcher for the Nonprofit EZIRS believes that
the IRS's claim is not correct and that it generally takes people longer to complete each of the
forms. She recorded the time (in minutes) it took 20 individuals to complete each form. The data
is given in the Excel spreadsheet on Blackboard.

Is there evidence to show that the researcher’s claim is correct?

For this you should:
(i) Construct a boxplot and histogram, with full graph and axis titles, to illustrate your
data, and describe how they relate to your results.
(ii) Check the normality of each sample to determine which test is appropriate.
(iii) For each form, you should perform a relevant test at the 5% significance level to see
if the central value of the time to fill it is greater than 160 minutes.
(iv) Construct corresponding two-sided confidence intervals for the mean/median for
each group and determine whether the results align with your hypothesis test.








Objective:
We wish to conduct a formal report for the IRS research, properly analyzing each of the three
samples (for forms A, B, and C, respectively) and determining a conclusion for whether any of
the three forms takes longer than 160 minutes to complete. You will do so by first determining
which statistical procedure you should use for each of the three samples. Note that you make use
the assumption that the variable is continuous (but normality is up to you to demonstrate).

It is understood that she has a fair understanding of introductory-level statistics, but nothing
beyond the scope of the basics taught in an intro course. Thus, it will be up to you to provide a
formal report that also describes the methodology in a way that is consumable to the client (so,
some colloquial descriptions are acceptable, as long as formal definitions are provided in an
appendix). Furthermore, the goal is to provide a substantive narrative for the researcher to follow
and effectively establishes a narrative with various title headers: Introduction, Statistical
Background & Terminology, Methodology, Results, Conclusion.

Grading
Grading for Paper 1 will comprise of three components:
(1) 5 Points for a complete version of the initial draft.
(2) 5 points for attendance of one-on-one conferencing over the initial draft.
(3) 50 points for the final draft.

This breakdown provides a total of 60 points
Formatting of the Paper:
• All papers must be roughly 4-6 double-spaced typed pages with 1-inch margins. Ideally,
it is desired to be written in Times New Roman 12-point font. A little under or a little
over is okay, but be cautious about not writing enough (for example, a solid conclusion
with its corresponding discussion should amount to a page on its own).
o Use headers to describe each of the following sections: Introduction, Statistical
Background & Terminology, Methodology, Results, Conclusion.
o Be sure to provide motivation and appropriate transitions between sections, as
well as to establish a narrative that aligns with both the formality as well as the
context of the researcher’s statistical understanding. Reminder – it is up to you to
narrate the process of your procedure, as so they can fully understand and
replicate it, if necessary.
• For the Introduction section:
o You should provide a brief overview of scenario as well as the situation of data
collection and values for which we are testing.
▪ Avoid determining whether we are testing a mean or median until later
when you test your assumptions.
• For the Statistical Background and Terminology section:
o Discuss the importance and use of statistical terminology, and make it flow as to
provide a narrative flow chart of what the researcher should know as she begin to
analyze the results.
o Be sure to use the following terms:
▪ Parameter, Statistic, Sampling Distribution, hypothesis testing, the
parametric test we can use (along with assumptions), nonparametric test
we can use (along with assumptions).
• For the Methodology section:
o Determine which statistical procedure you should be using, and provide both
appropriate graphs as well as statistical inference tests to determine which
procedure you need to produce. Produce your hypotheses in narrative form.
o Use this section to determine which test you will need to use for each of the three
forms, but hold off on your results until the next section.
• For the Results section:
o Now, with the given assumptions provided and knowledge of the procedure you
will perform, provide a narrative form for each hypothesis test and the
accompanying confidence intervals respective to the procedure needed.
• For the Conclusion section:
o Briefly summarize your paper and provide an overall conclusion for the casual
reader to read and obtain an understanding of your work.
o A minimum of two paragraphs will be necessary to properly summarize your
paper and results.
• All papers must include a title page that includes a report title, your name, instructor’s
name, course name, and date.
• Provide an Appendix with the following items:
o The complete code for which you used to produce your results.
o A glossary with full technical definitions of the following terms and formulas:
Parameter, statistic, sampling distribution, hypothesis testing, Shapiro-Wilk test,
t-test, sign test.
• IMPORTANT: Aside from the glossary portion of the appendix, no portion of the
main paper should be in bulleted or list form. As a reminder, this paper is to be a full
report and to represent a complete narrative. Inclusion of bullets or lists instead of
paragraph form will result in a reduction of the letter grade (see the Readability and
Formatting section of the rubric).
Sample Rubric for Paper 1, STA 2183W

Organization and Motivation: /10
(Motivate, introduce and discuss all relevant statistical concepts (and terms) appropriately)
10 -> Full discussion of the motivation and conclusion behind each procedure.
8 -> Notable errors that deter organization and understanding of procedures, but generally well-written.
6 -> Difficulty in understanding the procedures and the reasons behind the benefits and/or flaws.
4 -> Clear gaps in understanding the purpose behind the procedures and purpose of the report.
2 -> Insufficient discussion.
0 -> No discussion.
Readability and Formatting: /10
(Write well. Make transitions smooth and natural. Formulate a narrative that clearly expresses the
process.)
10 -> Clear writing with minimal errors.
8 -> Notable errors that deter readability, but generally well-written.
6 -> Difficulty in reading, notable gaps in logic and explanation.
4 -> Bullets with lack of paragraphs, clear gaps in logic and flow.
2 -> Insufficient writing.
0 -> No writing.
Appendix and SAS/R Results: /15
(Use SAS or R to do all calculations and copy those to your report. Put definition, interpretation and
important properties of expectation of random variables in an appendix. This part should sufficiently
help the beekeeper to understand the expectations you use to compare the three methods.)
15 -> Clear structuring of the Appendix & SAS/R results, aiding in the numerical comprehension.
12 -> Minor errors in computation or definitions that do not align with the paper.
9 -> Significant errors in the results and/or the information found in the Appendix.
6 -> Significant and incomplete data with incorrect explanations of the terminology in both sections.
3 -> Insufficient information.
0 -> No writing.
Statistical Terminology and Results: /15
(In particular, you must describe (or define) and explain Parameter, statistic, sampling distribution,
hypothesis testing, Shapiro-Wilk test, t-test, and sign test within the context of the paper.)
15 -> Clear and correct explanations of the statistical terminology and results.
12 -> Slight errors in explanation or interpretation, but a general understanding of each procedure.
9 -> Significantly incorrect results, notable gaps in logic and explanation and interpretation of results.
6 -> Significantly incorrect results with incorrect explanations of the terminology in the paper.
3 -> Insufficient results.
0 -> No writing or results.


Total: 50 Points