# Ib Extended Essay Statistics

I. Abstract In the study of mathematical statistics, there are different ways that a set of data can be proved to be a significant set. However, the ways that I am going to prove if the data is significant can be done in two different ways by using the z-proportion test and the Chisquare test (X2). These two significant tests can prove if a set of data is either significant or not significant. What is interesting about the three tests is that they are done in a very similar way yet end up with different results in regards to significance. In order to prove this thesis, I did an experimental test on the students at my high school. This experiment was done in order to create a sample problem. I will continually use this problem and it will be rephrased, reused, and integrated to represent the test being used. In this paper, the three tests’ formulas and development will be shown to gain an overall understanding of how the tests are similar. II. Creation of the Sample Problem A self conducted statistical experiment was done twice on same populations and data was collected and will be used as a sample question and integrated through this paper to their respective significance test. The question was conducted with a double-blind experiment in randomly selected classrooms. Double blind represents that both the experimenter and those receiving the soda have no idea on what soda they had received, therefore, eliminating the bias in the conducted experiment. Each building in Charter Oak High School has a letter on them (A, B, C, etc.). Firstly, all building letters on the Charter Oak High School was placed into a hat, then picked out and recorded. Then, a number from 1-9 was placed into the hat, representing the class room number. After this process, the room in one of the buildings was randomly selected to have an experiment conducted in their class for example, D-4. Two selected volunteers in the class would give the students cups with letters representing the soda brand...