Description
Write a Python function called sqrt2 that calculates and prints to the screen the square root of 2 to 100 decimal places. Your code should not depend on any module from the standard library[1] or otherwise. You should research the task first and include references and a description of your algorithm.
- The Chi-squared test for independence is a statistical hypothesis test like a t-test. It is used to analyse whether two categorical variables are independent. The Wikipedia article gives the table below as an example [4], stating the Chi-squared value based on it is approximately 24. Use scipy.stats to verify this value and calculate the associated p value. You should include a short note with references justifying your analysis in a markdown cell.
| A | B | C | D | Total | |
| White collar | 90 | 60 | 104 | 95 | 349 |
| Blue collar | 30 | 50 | 51 | 20 | 151 |
| No collar | 30 | 40 | 45 | 35 | 150 |
Total 150 150 200 150 650
- The standard deviation of an array of numbers x is calculated using numpy as np.sqrt(np.sum((x – np.mean(x))**2)/len(x)) . However, Microsoft Excel has two different versions of the standard deviation calculation, STDEV.P and STDEV.S . The STDEV.P function performs the above calculation but in the STDEV.S calculation the division is by len(x)-1 rather than len(x) . Research these Excel functions, writing a note in a Markdown cell about the difference between them. Then use numpy to perform a simulation demonstrating that the STDEV.S calculation is a better estimate for the standard deviation of a population when performed on a sample. Note that part of this task is to figure out the terminology in the previous sentence.
- Use scikit-learn to apply k-means clustering to Fisher’s famous Iris data set. You will easily obtain a copy of the data set online. Explain in a Markdown cell how your code works and how accurate it might be, and then explain how your model could be used to make predictions of species of iris
- References
- GitHub Inc., “GitHub,” https://github.com/.
- GMIT, “Quality Assurance Framework,” https://www.gmit.ie/general/quality-assurance-framework.
- McLoughlin, “Using git for assessments,” https://github.com/ianmcloughlin/using-git-for-assessments/.
- Wikipedia contributors, “Chi-squared test — Wikipedia, the free encyclopedia,” 2020, [Online; accessed 1-November-2020]. [Online]. Available: https://en.wikipedia.
org/w/index.php?title=Chi-squared test&oldid=983024096
[1] By the standard library, we mean the modules and packages that come as standard with Python. Anything built-in that can be used without an import statement can be used.
