CHI-SQUARE TEST OF INDEPENDENCE OF STUDENTS’ PERFORMANCE IN UME AND POST-UME .
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CHI-SQUARE TEST OF INDEPENDENCE OF STUDENTS’ PERFORMANCE IN UME AND POST-UME .
Chapter One: Introduction
1.1 Background of the Study
In 2005, the Federal Government, under former Minister of Education Mrs. Chinwe Obaji, implemented a policy of post-UME (University Matriculation Examination) screening in universities.
This policy required all tertiary institutions to conduct additional screening of candidates following the release of their UME results before to admission.
According to Obaji, candidates with a score of 200 or higher will be short-listed by Jamb, and their names and scores will be given to their preferred colleges, which will then conduct or execute another screening test in the form of aptitude tests, oral interviews, or possibly another examination.
Obaji measured the success of her policy by going on national media and showing incidents of students who scored 280 or above but did not score 20% in the post-UME screening. According to her, these pupils must have cheated during the Jamb examination and hence failed post-UME screening because there was no room for them to cheat or be impersonated.
Based on the then-Minister of Education’s strategy, the former Vice-Chancellor, Prof. E.A.C. Nwanze, implemented it by implementing university post-UME screening. Since then, the policy has proven tremendously effective at the university. Sitting for the screening exercise continues to require a score of 200 or higher.
The chi-square test is used to determine whether two or more population proportions are equivalent. The chi-square test is presented in terms of two aspects: chi-square goodness-of-fit and chi-square test of independence.
The chi-square test of goodness of fit determines if a specific theoretical probability, such as the binomial distribution, is a near approximation to a sample frequency distribution.
The test of independence is a method for determining if the hypothesis of independence between variables is plausible. This process checks for the equality of more than two population proportions.
Both X2 tests provide a result on whether a set of observed frequencies differs sufficiently from a set of theoretical frequencies to reject the hypothesis under which the theoretical frequencies were obtained.
The chi-square distribution theorem states that independent normally distributed random variables (X1, X2, … Xv) have a mean of zero and a variance of one (s2). The equation X21 + X22 + … + X2v = ∑ X2j represents X2 – j=1 distributed with v degrees of freedom.
Hypothesis testing is required before making any statistical decisions. Kreyszig (1988) defined a hypothesis as any acceptable assumption about a distribution’s parameters.
In statistics, it is usually impossible to test hypotheses on the entire population; instead, a sample is taken from the population and used to draw conclusions about the population. If the conclusion is not consistent with the given assumptions, the hypothesis is rejected; otherwise, it is not rejected.
Furthermore, the hypothesis testing technique in parameter statistics allows us to assess whether or not to reject a hypothesis or whether the observed sample differs significantly from the expected result. Hypothesis testing is the process of making decisions based on a sample.
According to Rao (1952, 1970), several attempts have been made to develop a consistent theory from which all significance tests can be inferred as solutions to precisely stated mathematical problems.
It is impossible to dispute whether such a theory exists or not, but formal theories that lead to a clear grasp of the issues are still vital. One such theory, developed by Neyman and Pearson (1928, 1933), is significant because it clarifies the different complicated problems in hypothesis testing and led to the creation of general theories in discriminating, sequential testing, and so on.
Many questions occur in the course of hypothesis testing, such as when a hypothesis should be rejected or not rejected. What is the likelihood that we will make the wrong decision, resulting in a consequential loss?
We can also inquire if two variables are independent or if a distribution follows a particular pattern. All of these questions are likely to surface during decision-making. However, the chi-square statistical test can provide answers to the above issues.
1.2 Objectives of the Study
1. To assess pupils’ capacity to carry out a study independently.
2. To demonstrate the usage of chi-square tests and its application to real-world problems.
3. To assist pupils comprehend the steps involved in decision making.
4. Help pupils comprehend hypothesis testing using sample data and making statistical inferences.
Significance of the Study
This study is extremely important for students in mathematics, social and management sciences, and any other managerial discipline or sector who want to comprehend the intricacies of the decision-making process utilising chi-square independence tests.
1.4 Scope of the Study
The scope of this study includes the University of Benin. Chi-square (c2) distribution after UME, test, and procedure for carrying out the c2-test.
1.5 Definition Of terms.
Some essential principles in statistical analysis include the following:
Ibrahim (2009) defined a population as a collection of existing entities (often people, objects, transactions, or events) that we want to investigate. A population can be finite or endless.
For example, the population of students in the mathematics department is finite, yet the population of all conceivable outcomes (heads or tails) in successive coin tosses is infinite.
Dass (1988) defines population parameters as statistical restrictions within a population, such as mean (µ) and standard deviation (s). Parameters are represented by Greek letters.
Ibrahim (2009) defined a sample as a subset of units in a population, i.e. a piece or part of the population under consideration. The method of picking a sample is referred to as a sampling procedure or plan.
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