In this project, you will perform a hypothesis test to determine the validity of a claim. You will either test a claim about a population mean (Sections 8-2 and 8-3) or a Proportion (section 8-4). (If you want to test a different kind of claim using one of the methods that we cover in Chapters 8 or 9, you must obtain approval from me.) You must follow the 7-step hypothesis testing procedure given in class. Details on the project (including a breakdown of how the project will be graded) are below.
You will type a paper detailing your work as outlined below (if you are unable to type your calculations, you can leave blank space in your typed paper and neatly handwrite your calculations). You will only turn in an electronic copy of your assignment, so if you do not type your calculations you must then scan the pages that contain handwritten parts and combine them with the rest (see Step 6 on how you should turn in handwritten pages). Most of your paper will be in a pdf titled "lastname-firstname-math243-project.pdf" (obviously, replace "lastname-firstname" with your name). A small part of your work will be in an Excel file titled "lastname-firstname-math243-project-data.xlsx" (see below in Step 2). Both the pdf and the Excel spreadsheet must be turned in to receive full credit.
You should include a title page containing your name and information about the course. Each numbered part below should be on a separate page. You can find a template word document
here. Feel free to use the template or type the paper from scratch.
- DEFINE PARAMETER (20 points): Define the parameter you are going to test. You must find a claim about a population mean or proportion in a source that is credible. You cannot make up your own claim. Make sure your source really is claiming what you say it is claiming. If you are unsure whether your source is credible, you are strongly encouraged to ask me about it in advance. See the end of this assignment for some examples to give you an idea of possible parameters to test. You may only test a different kind of claim if you receive approval from me ahead of time.
Write a paragraph in your paper to briefly explain the parameter that you have chosen to test, citing the source. If the source is a website, include the specific URL (not just the general "homepage" of the website) inside your Excel spreadsheet so that the source can be confirmed. If I cannot find the claim in the website that you cite, you will not receive credit for citing the source.
It is a good idea to do this step early and ask me (during office hours or through email/Canvas) whether you have chosen a suitable parameter to test. I will be glad to offer advice on whether your choice will likely work.
- GATHER SAMPLE (15 points): Once you have chosen a parameter, you must collect a sample to use in a hypothesis test. You must collect the sample yourself. You cannot use a sample that you found online or anywhere else; you MUST collect it yourself. If your sample is made up of people, you must include their names with your data. For example, if you are checking the average height of men, you must personally ask your sample of men to measure their heights for your sample, and then you must record their names and their heights.
If you are testing a claim about a mean, you must collect a sample of size at least 30. If you are testing a claim about a proportion, you must collect a sample of size at least 100.
Briefly describe in this step your method of gathering the sample. All sample data must be provided in the Excel spreadsheet. Name the spreadsheet "lastname-firstname-math243-project-data.xlsx" and submit it through this Canvas assignment.
- CALCULATIONS (5 points): If you are testing a mean, calculate and record the sample mean and sample standard deviation (note: if your source includes a population standard deviation, then you may use it, but you must include it in your description in Part 1 above). If you are testing a proportion, calculate the sample proportion.
Include all calculations in your paper (if you are unable to type your calculations, you can leave blank space in your typed paper and
handwrite your calculations, but see Step 6 on how you should turn in handwritten pages). You can have Excel sum your columns if you wish (if you do, include that work in your spreadsheet). State in this step what the sums were and then plug them into the appropriate formulas in this step.
After your calculations, you should clearly state the calculated sample data (mean, standard deviation, or proportion as appropriate to your test) at the bottom of this step.
- HYPOTHESIS TEST (40 points): Using the 7-step procedure for hypothesis testing given in class, test the claim from your source using your sample. Test the claim at confidence level α=0.05. Use the appropriately tailed test (2-tailed, right-tailed or left-tailed) to match the claim. Use the correct test (z-test for mean, t-test for mean, z-test for proportion) for your data.
Be sure to clearly outline your work following the 7 step. If you are unable to type any steps containing calculations, you can leave blank space on those steps, print the page, neatly handwrite your calculations, and scan the page, but see Step 6 below on how you should turn in handwritten pages.
- CRITICAL THINKING (10 points): Give a non-mathematical argument (at least a few sentences) as to why or why not you think the hypothesis was or was not rejected. Your explanation should make it clear that you understand what rejecting (or not rejecting) H0 means for your test. You should include a well-thought-out reason why the test might have turned out the way that it did. Be sure your answer reflects what your test actually found (for some reason people often reject the claim and then proceed to explain why it was not rejected, or vice versa).
- OVERALL PROJECT (10 points): Neatness, clarity, and organization must be present throughout the paper. Spelling and grammar should be correct. Make sure you include a title page and that Steps 1-5 listed above are each on their own page.
To avoid penalties, you must upload 2 files following the guidelines below:
- A 6-page pdf titled "lastname-firstname-math243-project.pdf" (but change it to your name).
Your pages should be as follows:
If you print and handwrite any calculations, you must scan those pages and re-combine them with the rest of your pdf. Do not print and scan the fully-typed pages.
is excellent for easily combining pdfs and arranging their pages in the correct order.
| ||Page 1: ||Title Page.
| ||Page 2: ||Define Parameter (Step 1)
| ||Page 3: ||Gather Sample (Step 2)
| ||Page 4: ||Calculations (Step 3)
| ||Page 5: ||Hypothesis Test (Step 4)
| ||Page 6: ||Critical Thinking (Step 5)
- An Excel spreadsheet titled "lastname-firstname-math243-project-data.xlsx" (but change it to your name).
If your claim in Step 1 came from a website, include the full URL in the spreadsheet.
Include all sample data in the spreadsheet.
Turn in the actual spreadsheet, not a pdf printout of the spreadsheet.
Means: Average height of adult men. Average age of college students. Average GPA of athletes. Average amount of soda in a can.
Proportions: Proportion of people with blood-type O. Proportion of college students with student loans. Proportion of skittles that are red.
These are meant to give you a basic idea of types of claims, but you should try to find a claim that is interesting to you.
DO NOT do a claim about height. I am tired of reading 10 of the same paper every semester.