**IB Math Studies Internal Assessment**

Mathematical Processes

Chi Squared Test

Information/ Measurements

Validity

Despite the fact that not all of the techniques that I used fit the data very well, they were still valid tests to prove a lack of certain types of correlations like linear, disproving what I initially thought the data would show. This caused all of the tests to be valid despite not fully proving or disproving anything.

The main problem with the data that could lead to error was the vague rating system for happiness that could be interpreted in different ways or could be affected by the person's current mood, as apposed to their overall happiness.

Overall, the results can be interpreted meaningfully as they are generally accurate, but the data is not as accurate as it could be and more tests could be done to find different types of correlation that may not appear through the chi squared or linear regression tests.

Interpretation of Results

Despite the results of the tests I conducted saying there is little to no correlation between the two variables, I feel like there still might be some correlation that cannot be shown through the tests that I did. There are a lot of external factors that could have affected the results, so more tests would have to be done to fully disprove my hypothesis. Overall, my results show no correlation, but more could be done to completely disprove my hypothesis.

**Introduction/ Hypothesis**

Topic: Happiness vs. Number of Advanced Classes Being Taken

Hypothesis: There is a correlation between the number of advanced classes being taken and one's level of happiness

I chose this topic because I have taken a mix of advanced and on-grade classes throughout high school and was curious as to how this would affect people's happiness and if one would be happier due to the payoff of the hard classes or happier with a less heavy work load.

I gathered my data through surveying a random group of people and asking how many advanced classes they were taking and their level of happiness on a scale from one to ten

I used the chi squared test, linear regression, and Pearson's product moment correlation coefficient to test correlation.

Linear Regression Test

Pearson's Product Moment Correlation Coefficient

Null and Alternative Hypothesis:

H0= One's happiness level is independent of taking more advanced classes

H1= One’s happiness level is dependent/ not independent of taking more advanced classes

degrees of freedom= 54

Critical Value at .05 significance = 38.1162

Chi Squared value=33.5471

33.5471<38.1162 so accept null hypothesis and reject alternative hypothesis

The test disproved my hypothesis, but was not too far off, meaning there could still be some correlation despite the chi squared test forcing me to accept the null hypothesis

y=ax+b

a=-.0313253012

b=7.288915663

r=-.0298691386

This data definitely disproves my initial thesis of their being a linear relationship, but does not necessarily disprove there being no correlation due to not all correlations being linear

My r value was -.0298691386 or -0.03 to 3 significant figures. Therefore, my variables had a very weak correlation, almost having none.

Despite this data saying the correlation is almost nonexistent, the Chi Squared test was very close and was not nearly as far away from accepting the alternative hypothesis, possibly meaning my hypothesis could still have some merit. This also indicates that there could be a correlation other than a linear one.