EmergingTechnologies - Emerging Technologies -Solved

Instructions
Four tasks will be listed here at different times during the semester. You should complete all tasks in a single jupyter notebook. This, along with relevant files like a README, should be in a single git repository synced with a hosting provider like GitHub [1]. That URL should then be submitted using the link on the Moodle page.

1. 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.

2 .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 24.6. 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

3.    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.

4.    NB – when I first posted this task, I accidentally wrote “k-means” where I meant to write “kNN” for k Nearest Neighbours. Because of this, I will allow either algorithm to be used and have extended the deadline by two weeks. 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.



[1]   GitHub Inc., “GitHub,” https://github.com/.

[2]   GMIT, “Quality Assurance Framework,” https://www.gmit.ie/general/quality-assurance-framework.

[3]   I. McLoughlin, “Using git for assessments,” https://github.com/ianmcloughlin/using-git-for-assessments/.

[4]   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.