Introduction
1.1 Background of the Study
The Federal Government in the year 2005 through the former Minister of Education, Mrs. Chinwe Obaji, introduced the policy of post-UME (University Matriculation Examination) screening by Universities. This policy mandated all tertiary institutions to carry out the task of further screening candidates after their UME result before giving admission. According to Obaji, candidates with a score of 200 and above will be short-listed by Jamb and their names and scores sent to their universities of choice which should then do or undertake another screening test in form of aptitude tests, oral interview or even another examination. Obaji measured the success of her policy by coming on national television to show cases of students who had scored 280 and above but could not score 20% in the post-UME screening. According to her, these students must have been engaged in cheating during Jamb examination and so could not pass post-UME screening because there was no room for them to cheat or be impersonated.
Based on this policy of then Minister of Education, the former Vice-Chancellor, Prof. E.A.C. Nwanze implemented the policy by introducing the university post-UME screening. Since then, the policy has been highly effective in the university. 200 scores and above remain the benchmark of sitting for the screening exercise.
Chi-square test provides the basis for judging whether more than two population proportions may be considered to be equal. Chi-square test is discussed by considering two aspects, such as chi-square goodness-of-fit and chi-square test of independence.
Chi-square test of goodness of fit provides a means for deciding whether a particular theoretical probability such as the binomial distribution is a close approximation to a sample frequency distribution, while test of independence constitutes a method for deciding whether the hypothesis of independence between different variables is tenable. This procedure provides test for the equality of more than two population proportions. Both X2 tests furnish a conclusion on whether a set of observed frequencies differs so greatly from a set of theoretical frequencies that the hypothesis under which theoretical frequencies were derived should be rejected.
1.2 Statement of Problems
Investigation reveals the following problem of the Chi-square test of independence of students' performance in UTM and Post-UTM research work;
- Lack of proper test of students’ independent ability in carrying out a study.
- Improper investigation of students with the use of chi-square tests and its application to real life problems.
- Insufficient information relating to students’ understanding with respect to decision making process.
- Incorrect administration of hypothesis testing on the basis of sample data and make a statistical inference.
1.3 Objectives of the Study
The following are the specific objectives of the Chi-square test of independence of students' performance in UTM and Post-UTM research work;
- To test students’ ability in carrying out a study independently.
- To show students the use of chi-square tests and its application to real life problems.
- To help students understand the process involves in decision making.
- To assist students to understand hypothesis testing on the basis of sample data and make a statistical inference.
1.4 Research Questions
The following research questions will be raised in this study:
- Does the independence of students in UTM and Post-UTM influence their academic performance?
- Will there be any difference in the academic performance of students in UTM and Post-UTM?
- Is there any difference in the academic achievement of students’ independence in UTM and Post-UTM?
1.5 Research Hypothesis
The following research hypotheses will be formulated and tested in this study:
Hypothesis One
H0: There will be no significant difference in the performance of students’ independence in UTM and Post-UTM.
HA: There will be a significant difference in the performance of students’ independence in UTM and Post-UTM.
Hypothesis Two
H0: There will be no significant difference in the academic achievement of students’ independence in UTM and Post-UTM.
HA: There will be a significant difference in the academic achievement of students’ independence in UTM and Post-UTM.
1.6 Significance of the Study
This study is highly significant to students in mathematics, social and management sciences and all other managerial discipline or field of understanding the nitty-gritty of the process involved in decision making using chi-square independence tests.
1.7 Scope of the Study
The scope of this study covers the University of Benin Post-UME, chi-square (c2) distribution, test and procedure for implementing c2-test.
1.8 Limitations of the Study
During the course of this study, many things militated against its completion, some of which are:
- Time Constraint: The time frame given to accomplish this project was very short due to school academic calendar and it was carried out under pressure which made the researcher not to implement some necessary features.
- Establishment Policies: Establishment policies posed a serious limitation as most staffs are not ready to release information needed for this project work. There were lots of information needed from the staffs of this institution to enhance the study which took them time to release or they did not release at all for security purposes, hence the scope was reduced.
1.9 Definition of Terms
The following are some of the important concepts in statistical analysis:
