# IB Math Studies Chi Square IA

**Topics:**Null hypothesis, Statistical hypothesis testing, Pearson's chi-square test

**Pages:**10 (1420 words)

**Published:**February 23, 2014

Predictability of Social Media Usage to Grade Averages

IB Math Studies

Spring 2013

Table of Contents:

Introduction/Purpose……………………………………………………………..p.3

Data Collection Method……………………………………………………….....p. 3 - 4

Data Analysis: Chi-Squared Statistic

Frequency Table…………………………………………………………p. 4 - 5

Contingency Table……………………………………………………….p. 5 – 6

Chi – Squared Statistic…………………………………………………...p. 7

Degrees of Freedom………………………………………………………p. 7

Critical Value……………………………………………………………..p. 7 – 8

Conclusion……………………………………………………………………....p. 9 - 10

Introduction/Purpose

Predictability is the degree to which a correct prediction or forecast of a system’s state can be made quantitatively. It is necessary to achieve maximum productivity or potential when completing a task. The ability to foresee an occurrence before others allows one to alter different aspects in time to garner the utmost productivity. The question that has been plaguing today’s generation is the use of social media sites, and their consequences on our lives. A restaurant only orders an amount of food adequate for its needs. If the restaurant orders more than it needs, then the extra food will spoil and the restaurant will lose some of its inventory. A trader that has inside information on a corporation may sell his stock minutes before the price drastically falls, saving himself a loss of hundreds of dollars. Likewise, a student able to predict his or her grade depending upon social media usage would hold a valuable asset in determining what students need to do in order to pursue a particular grade average. I will conduct my project on the principle that students spend time on popular Web sites like Twitter or Facebook on a daily basis and the affect will appear on the outcome of his or her grade (per semester). Is there a significant correlation between a student’s average grade and the time spent on social media websites? I hypothesize that the student’s average grade will be dependent upon time spent on social media sites. To further my investigation, I will use a frequency table and contingency table to consider the situation if grades are dependent on time spent using social media sites. Data Collection Method

I conducted my research by creating a survey for 200 randomly selected high school students to complete. I will compare the 200 students, differentiating them between time spent on social media sites and the average grade received per semester. To compare my data, I will create two tables: a frequency table and a contingency table. One will represent the exact number of students surveyed and the other will show the association between the two variables. Survey:

CIRCLE ONE: What is your average grade (in a semester)? A B C D F(or below) CIRCLE ONE: How much time do you spend on the computer/social media sites? Less than 1 hour1-2 hours2-3hours3 hours or more

Data Analysis

Frequency Table:

In the given situation, the question at hand is “how much time do students truly spend on social media sites?” The results in the frequency table below summarize the sample of 200 randomly selected high school students, their grades, and their time spent on social media sites:

A

93-100

B

85-92

C

77-84

D

70-76

F

Below 70

Total

Less than 1 hour

23

5

3

3

2

36

1 – 2 hours

34

13

14

5

0

66

2 – 3

hours

16

27

18

4

1

66

3+

hours

13

4

2

7

6

32

Total

86

49

37

19

9

200

After placing my collected data in table form, I calculated the sum of each number of students’ grades and the time spent on the computer using social media sites. Contingency Table:

Tables such as these, in which the number of observations are entered according to two different factors (or classifications) are called contingency tables. The question to be answered is, “Are grades and time spent (daily) on...

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