The Golden Ratio, sometimes referred to as Phi (, is a ratio between two lengths A and B that yield the exact number which is irrational and is approximately We will use 1.62 as our approximation for the purposes of this hypothesis test. Many claims have been made that the golden ratio exists in nature both in living and non-living things.For example, the length of a human arm from elbow to wrist compared to the length of the hand from wrist to tip of middle finger. In this example, the length from elbow to wrist would be length A and the length from wrist to middle finger would be length B.To test a claim such as this, suppose we collected a large data set and fond the mean average ratio for all the ratios collected to be 1.71. This is indeed close to 1.62, but do we then agree with the claim that human arms and hands grow in an approximate golden ratio? What if the original claim was that this human ratio was which is approximately ? Do our findings support this claim? This example shows why we never, ever support the null hypothesis with our findings. We may only reject it due to strong evidence to the contrary, or fail to reject it due to insufficient evidence to the contrary.
For this example we would have the following:
Notice that we are using the claim that the ratio of arm length to hand length is in the golden ratio as our null hypothesis. This may seem strange, but it is the only way to proceed since we would have no other default position for the null hypothesis. Therefore our test may only reject this claim or fail to find sufficient evidence against it (which is not the same as supporting the claim).
For this project we will not use human ratios, but rather natural objects that are readily available to you. Search out items that you have access to that are abundant enough to enable you to find a random sample of 30 or more that represents a much larger population. Measure two different lengths on the object and compute the ratio (long/short). Try different objects until you get initial measurements that yield a ratio very close to 1.62.
Example: Suppose I walk around my backyard and measure the width and length of an apple leaf and find the ratio is only 1.2. This is not even close to 1.6 so I move on to an oak leaf. The ratio is 1.4, again not close enough so I move on to an ivy leaf. The initial ratio (from one leaf) is 1.64, eureka! This is close enough to 1.62. From this initial finding I settle on using ivy leaves for this test. Thus, my null hypothesis is that the mean ratio of the length to width of all ivy leaves is 1.62 (our approximation of the golden ratio). Next, I come up with a way to randomly select 30 or more ivy leaves of the same species (different plants if possible). I create a data table of all the measurements and ratios I calculated for each leaf. I do not measure each leaf as I go and only include those that are close to 1.62. I collect 30 or more and then measure them all and whatever ratio I find is what gets entered into the data table.
|Leaf #||Side A (long side)||Side B (short side)||Ratio A/B|
I now use the Ratio A/B column to calculate all of my summary statistics, such as mean, median, standard deviation, Q1, Q3 and so on. I use online tools such as StatKey to evaluate the claim (more on that later) and decide if I shall reject the claim or fail to reject the claim due to insufficient evidence.
Your Project: Using the example above, locate an item to generate a claim and then test the claim using statistical tools. What follows is a scaffolding of how to arrange your findings for your formal report that is to be turned in as a word.doc or PDF. Do not write in bullet point format.
The Formal Report: Each student must turn in his or her own unique report. I would like to read your thoughts and in your words. You are allowed and encouraged to discuss your ideas with classmates, the math tutoring center, the writing center, and myself during office hours. Please DO NOT email me any rough drafts. I also recommend that you never email a classmate your report file or a link to a Google drive. The report will be 12pt type, Arial or Calibri font, and 1.15 to 1.25 line spacing. Use the bolded headings below for your report, in the exact order displayed. Do not use bullet points in your writing. Embed all tables and graphs in-line (meaning place them near the text where they are referenced). Use screen capture (image clipping) for graphical displays from StatKey. Size the images to make them readable. There is no minimum or maximum length to the report. It should be as long as is needed. I highly recommend that you visit the writing center and allow someone to review your work for clarity.
Abstract: This is a brief summary of your findings. Include all metrics such as p-values, t-statistics and confidence intervals and what they mean in the context of the investigation (briefly). You will typically write this last even though it comes first in the report.
In regards to the ratio of the length vs. the width of the common ivy leaf (Hedera), we found statistically significant evidence, p-value=0.001, that this ratio is different from 1.62. Additionally, we estimate the true parameter of this ratio to be between …
More can be said here, but should be 3 to 6 sentences.
Introduction: Here is where you introduce the reader to the study. Give some background on the golden ratio. State the statistical question of interest. What are you investigating? What parameter are you trying to estimate? What methods did you use (box plot, p-value…)? What randomization technique did you use when collecting data (this is important)? Include one image of the overall objects you are colleting. Example: If you are collecting ivy, take a picture of the overall ivy bush and include it in the report. Also include an image, or two, of how you are measuring the length and width of the objects. Example: If you are measuring ivy leaves, you might show a picture of an ivy leaf flat on a table with a ruler indicating what you are considering to be length and width.
Histogram and Boxplot Analysis Using Summary Statistics:
Example: Here is the histogram for an underlying data set.
(This example is not about the golden ratio):
Example: Here is the boxplot for an underlying data set.
(This example is not about the golden ratio):
What do you think this number is describing? What number do you think is a large, or small, amount of variance?
Hypothesis Test, Confidence Interval and Conclusions:
Bias and Critiques: In this section you should critique your own work. How well do you think your randomization scheme worked in preventing bias? Describe at least one form of bias in your data set (there will be at least one). What would you do to improve it next time? How accurately do you think your measurements were? What could you do to improve this? Do you believe your conclusions are reliable based on the underlying data set? And anything else you would like to improve or do differently in the future.
Personal Reflections: (there is no right or wrong here, except to leave it blank)
○ What parts of this project were difficult for you? Were there technology issues that got in your way? Did you find the writing center/math tutoring helpful (if used)?
○ What did this project help you understand about these statistical tools?
○ What do you think this project measures about you and your understanding of the material and in what way is this measurement different from a timed exam (is this more work)?
○ How could this project be improved?
Data Set: Embed a table containing all of your measurements and data.
***Notes to you:
For more information on Hypothesis Testing the Golden Ratio read this:https://en.wikipedia.org/wiki/Golden_ratio
Why Choose Us
At Acme Writers, we always aim at 100% customer satisfaction. As such, we never compromise o the quality of our homework services. Our homework helpers ensure that they craft each paper carefully to match the requirements of the instruction form.
Professional Academic Writers
With Acme Writers, every student is guaranteed high-quality, professionally written papers. We ensure that we hire individuals with high academic qualifications who can maintain our quality policy. These writers undergo further training to sharpen their writing skills, making them more competent in writing academic papers.
Our company maintains a fair pricing system for all academic writing services to ensure affordability. Our pricing system generates quotations based on the properties of individual papers.
Acme Writers guarantees all students of swift delivery of papers. We understand that time is an essential factor in the academic world. Therefore, we ensure that we deliver the paper on or before the agreed date to give students ample time for reviewing.
Acme Writers maintains a zero-plagiarism policy in all papers. As such, Acme Writers professional academic writers ensure that they use the students’ instructions to deliver plagiarism-free papers. We are very keen on avoiding any chance of similarities with previous papers.
Customer Support 24/7
Our customer support works around the clock to provide students with assistance or guidance at any time of the day. Students can always communicate with us through our live chat system or our email and receive instant responses. Feel free to contact us via the Chat window or support email: support@Acme Writers.
Try it now!
How it works?
Follow these simple steps to get your paper done
Place your order
Fill in the order form and provide all details of your assignment.
Proceed with the payment
Choose the payment system that suits you most.
Receive the final file
Once your paper is ready, we will email it to you.
Our writers complete papers strictly according to your instructions and needs, no matter what university, college, or high school you study in.
Our Homework Writing Services
Acme Writers holds a reputation for being a platform that provides high-quality homework writing services. All you need to do is provide us with all the necessary requirements of the paper and wait for quality results.
At Acme Writers, we have highly qualified academic gurus who will offer great assistance towards completing your essays. Our homework writing service providers are well-versed with all the aspects of developing high-quality and relevant essays.
Admission and Business Papers
With Acme Writers, we will help you secure a position at your desired institution. Our essay writing services include the crafting of admissions papers. We will still help you climb your career ladder by helping you write the official papers that will help you secure a job. We will guide you on how to write an outstanding portfolio or resume.
Editing and Proofreading
Acme Writers has a professional editorial team that will help you organize your paper, paraphrase it, and eliminate any possible mistakes. Also, we will help you check on plagiarism to ensure that your final paper posses quality and originality.
Acme Writers harbors professional academic writers from diverse academic disciplines. As such, we can develop homework writing services in all academic areas. The simplicity or complexity of the paper does not affect the quality of homework writing services.