**Students Prjoect (Spring 2018-2019)-****Chi-Square Tests with Applications**

**Students**

Shaimaa Falah Faisal U15105148

Najla Faiek Abu Saleh U15105422

**Abstract**

Testing relationships between categorical or qualitative variables for real-life is one of the important approaches of statistics for analyzing data which is widely used today.

Chi square distribution is a type of cumulative probability distribution, which provide the probability of every possible value that may occur. Chi square test is a statistical procedure derived from the chi-square distribution to compare the goodness of fit of theoretical and observed frequency distributions or to compare nominal data derived from unmatched groups of subjects.

In this project, we thoroughly demonstrated the concept of statistics and the main areas and types of statistics. The element of hypotheses testing with the methods concerning in p-value approach to specify the rejection and non-rejection regions then determine the types of errors will occur when reject or not reject. Explain Proportion for population in more details and present the procedure to perform tests of hypotheses for one sample and two samples both provided by a complete example. Moreover, we will discuss the case where there are more than two samples which is the Chi-square test, and this is the main topic of this research. We will discuss the chi square distribution, contingency table and goodness of fit test. A case study is included and used to apply all the illustrated theory using SPSS software. The results are shown in complete details.

Ragad W.A. Albarghash

There are two main opposing schools of statistical reasoning, frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong impulse that is starting to change the situation. The basic notions about these two approaches to inference are presented and the corresponding terminology is introduced.

Two main methods of statistical inference can be found in the literature of statistics. The first one is known as the frequentist (or classical) approach. This approach has been studied in 1440-361 (Mathematical Statistics). The second method to inference, which will be the choice of this project, is called the Bayesian approach. This approach can be viewed as the modern statistics to inference and it differs from the classical one in that it specifies a probability distribution for the parameter(s) of interest. The goal of this project is to extend the one-parameter Bayesian approach to the Multi-parameter case. Examples and real life applications are also considered. Section 1 - Section 6 are done jointly with Israa Alhamarna and Ragad Albarghash.

.