# Math Assignment Due By 7 Febb expert math SCMA 1000 – Business Statistics Winter 2022 Assignment 1 Introduction This assignment is intended to

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expert math

Winter 2022

Assignment 1

Introduction

This assignment is intended to give students the opportunity to use real data they gather themselves to help their understanding of how the tools and techniques taught in the first half of the course can be applied. Since I believe discussion and practice are important to learning, this assignment may be done by an individual alone or by a pair of student working together. Larger groups are not permitted without special permission.

Realize that it may seem like splitting up the different questions and doing them separately (or even having one person do all the work) is the best use of your time. Besides, I will not be able to tell if that is what you did. However, you will not learn what I hope you will learn from the activity and that will likely be reflected in your exam score. It is expected that both members of the team will have discussed the answers to each question before the assignment is completed.

Whether you work with someone else or by yourself, you must create a group (even just a group of 1) for assignment 1. If you do not create a group, you will not be able to download the template required for your answers or post you answers after you complete them.

If you have been looking at the text and kept up with the course content, this assignment should be very easy to do and should not take very long.

To do the assignment students will perform the following steps:

· Choose something to measure.

· Decide how they are going to collect data on this relationship.

· Collect a small set of data

· Analyze the data collected using graphical techniques (Chapter 2) and descriptive numerical statistics (Chapter 3).

· Determine if a linear relationship exists between the two variables measured.

· Complete a 2 stage tree diagram.

· Propose a directional relationship between the two variables and make predictions about the value of one variable based on the value of the other variable

Specific Steps

1) Overview

a) Choose something to measure. – This is totally up to you. If you are interested in stocks, you could look at the stock prices for two different stocks over time. If you are interested in basketball, you could look at the qualities of players like age and points scored. If like music you could ask your friends to rate songs from one to 10 and then estimate how many times they listened to the song that day. What you measure is not important.

b) However, here is what is important:

i) There must be 15 elements in your sample. (If you do not comply with this requirement, I will NOT be able to grade your assignment.)

ii) There must be three variables for each element:

(1) Two of these variables must be quantitative (numerical).
(Special note: While time of day is a quantitative variable, it is difficult to use in this format so try not to have that as one of your variables.)

(2) One must be categorical (qualitative). This variable should not have more than 4 categories. If you have more than 4 categories, you do not understand the concept.

c) Here is an example.

[Because I have used this here it MAY NOT be used in a submitted assignment.]

I am interested in the Canadian dollar’s performance against my home country currency (USD) and against another world standard (EURO). Each of those is an exchange rate which is a quantitative variable. I look these up on the internet and in less than ten minutes I have all the data I need

 Date 1 USD -> CAD 1 EUR -> CAD 2011-10 1.01982500 1.4000 2011-11 1.02581905 1.3895 2011-12 1.02378500 1.3470 2012-01 1.01326190 1.3068 2012-02 0.99652857 1.3194 2012-03 0.99385455 1.3126 2012-04 0.99263000 1.3066 2012-05 1.00984091 1.2918 2012-06 1.02807143 1.2892 2012-07 1.01393333 1.2445 2012-08 0.99214091 1.2307 2012-09 0.97829474 1.2604 2012-10 0.98720455 1.2808 2012-11 0.99704762 1.2801 2012-12 0.98956842 1.2976

d) In my case I will create a categorical variable but you might also gather it directly. For example if you are asking your friends about music, you might also ask them if they think the song is “Getting Old”, At Its Peak”, or “Just Coming On”

e) For my example, I am interested in knowing if the Canadian dollar is going up or going down and it can go up against both currencies together (Up), go up against one but not the other (Mixed), or go down against both currencies together (Down)

 Date 1 USD -> CAD 1 EUR -> CAD direction 2011-10 1.01982500 1.4000 Down 2011-11 1.02581905 1.3895 Mixed 2011-12 1.02378500 1.3470 Up 2012-01 1.01326190 1.3068 Up 2012-02 0.99652857 1.3194 Mixed 2012-03 0.99385455 1.3126 Up 2012-04 0.99263000 1.3066 Up 2012-05 1.00984091 1.2918 Mixed 2012-06 1.02807143 1.2892 Mixed 2012-07 1.01393333 1.2445 Up 2012-08 0.99214091 1.2307 Up 2012-09 0.97829474 1.2604 Down 2012-10 0.98720455 1.2808 Up 2012-11 0.99704762 1.2801 Mixed 2012-12 0.98956842 1.2976 Mixed

(Note – I had to go back to the website to be able to determine the first category.)

*****You now have all the information you need to complete the assignment.*****

Your data must be properly entered into the Excel template provided or my scoring program will not work.

Here are the questions;

Question 1
– Use words and describe your data and its relationship. This should be short and simple. What are your elements, what are your three variables and how did you find or measure them? When you do this you are providing me with enough information to know if you did the rest of the assignment correctly but I can’t/ don’t want to have to read pages to find the answer.

Question 2
– Indicate the scale of measurement for each of your variables. If you don’t know what this means, refer to Chapter 1.

Question 3
– Create a data table based on your observations. If you do not follow the data table structure as taught in class, I will not grade your assignment. You must also put you data into the template I have created in the way in the template requires. Failure to do this will mean that my scoring sheet will not work. This makes me very unhappy! Again what goes into a data table and how it is organized was covered in the first week. Values must be entered into the table as it exists in the template. Do not change the spacing or put more than one piece of information into a cell. Do not use any non-numeric characters (like commas, dollar signs or dashes). If you do this, Excel will determine that your number are not numbers and will give me error messages. Excel is used to automatically score your assignment and violating these rules will require manual scoring. This makes me very unhappy!

Question 4 a, b, c
– Using techniques introduced in Chapter 2 – create graphical analyses of your data. I want to see at least one histogram and one bar chart. Make sure the data you graph is appropriate for the type of graph you will use. What you do with the third variable is up to you. Please realize that a chart with 15 points on it is NOT a histogram or a bar chart. You must decide how to group the data into classes before you can make a histogram. Again, refer to Chapter 2 for instructions. Note: To create a histogram, you will have to create a classification table in addition to the raw data table. Second Note: Each graph must use one and only one variable. Graphs showing a relationship between two variable graphs occurs later in the assignment.

Question 5 a, b, c
– Prepare a set of descriptive statistics. I have asked for three different types of statistics; those that define the centre of the variable; those that define the shape of the distribution (how wide, how slanted, etc.) and any others you might think are useful. This is Chapter 3a although if you explore a little, you can find more than 4 statistics to calculate. There may be more lines than there are descriptive statistics. Again, each column must report on one and only one variable.

Question 6
– Create a box and whisker plot for at least one of the variables. Creating this data representation for the categorical variable will result in an immediate 0 for this section. Can you tell me why?

Question 7
– Use statistical techniques (numbers – no words or graphs) to determine whether or not a linear relationship exists between your two quantitative variables and how strong that relationship is. Again, this is Chapter 3 and you been doing this type of calculation since Grade 7 but you must think about what I am asking for.

Question 8
– Show the relationship between the two variables graphically. What conclusions can you draw from this? Does it give the same result as Question 7?

Question 9
– What is the probability for each condition of your categorical variable? This is Chapter 4. You must build a frequency table for your variable and draw a two stage tree diagram that presents the same data. In order to produce the second stage, you will have to convert one of your quantitative variables into categories and fewer is better.

Question 10
– Draw some conclusions about your data set. Do you think it is normally distributed, why or why not? Do you think that one variable causes a change in the other? Is this supported by your results?

All assignments must be submitted electronically using the dropbox on the website and the template provided there. Hard copy assignments WILL NOT BE GRADED!!

CRITICAL – The only types of files the dropbox will accept are .doc, .docx, .xls, .xlsx. If you try to use any other format, you will not be able to upload your files.

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