In this study, we are interested in comparing the mean performance of the male and female student in the mathematics subject. The data to be used in the study was collected from university of Manitoba. The researcher decided that both male and female students performed equally well in the subject of mathematics. The researcher decided to test this hypothesis using independent sample t-test. According to Gardiner, W. P. & Gettinby, G. (1998), independent sample t-test is used when the variables tend to be normally distributed. In this case according to Ott, L. & Longnecker, M. (2010), the assumption of equal variance is assumed and then tested the validity of the assumption. In this case, an independent samples t-test is the most widely used test statistics since it’s probably the most commonly known. It’s usually simple to use, simple, and can be incorporated by wide range of day to day situations. It advantage is that the researchers can be able to compare two phenomenons of two variables at time, with the aim of finding solutions to basic questions: one, if there is any relationship between the two variables, is there any effect if we change the level of one variable. And finally, distinguish if the two variables are related at any different level of the other variable.
The data was collected by interviewing 20 fourth year student from the University of Manitoba. The interview was conducted to determine the average performance of the students in their last four mathematics examinations. The researcher requested the respondents to provide the academic documents to reduce the errors chances. The table below shows the marks of the students’ in the mathematics subjects in the last 2 years.
The mean performance of both male and female perform equally well in mathematics subject
The alternative hypothesis
The mean performance of both male and female differ significantly.
Analysis and interpretations
An independent paired sample t-test is conducted to determine if there is any significant difference between the mean performance marks of male and female in the mathematics subject. The output of the analysis is provided below
Result and discussion
In each of the cases, the samples are independent of each other, in that they are separate samples containing a different set of data. The measurement of female marks in mathematics subject is not linked to the measurement marks of mathematics subject of the male students. And also measurement of male marks in mathematics subject is not linked to the measurement marks of mathematics subject of the female students. The t-test that will be in this study will be used to examine the difference between the mean marks of the mathematics in the female students and the mean marks in the male students. In this study, the assumption of normality and that the two samples they are composed of equal-interval hold. From the above results, the mean performance of male students is 67.3 while the mean performance of the female student is 67.7. The difference in mean performance is equal to 0.4, and the confidence interval in the difference in mean is (-1318, 1238). A t-test of the difference in the mean at null hypothesis is difference is zero against the difference is not equal to zero. The t-value is -0.07 with a p-value of 0.948. Since the p-value is larger than the confidence level of 0.05, we fail to reject the null hypothesis and conclude that the mean performance of both male and female in mathematics is the same. We thus conclude that the difference in the mean performance of male and female in the mathematics subject has no difference.
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Gardiner, W. P. & Gettinby, G. (1998) Experimental Design Techniques in Statistical Practice: A Practical Software-based Approach. Horwood Publishing.
Holmes, D., Moody, P. & Dine, D. (2011) Research Methods for the Biosciences. Oxford
Ott, L. & Longnecker, M. (2010) An Introduction to Statistical Methods and Data Analysis, 6th
International Ed. Brooks/Cole Cengage Learning.
Ruxton, G. D. & Colegrave, N. (2011) Experimental Design for the Life Sciences, 3rd Ed. Oxford
The table of the mean performance of the mathematics subjects for male and female students.
Independent Two-Sample T-Test and CI: male, female results
Two-sample T for male vs female
N Mean StDev SE Mean
Male 10 67.3 13.6 4.3
Female 10 67.7 13.6 4.3
Difference = mu (male) - mu (female)
Estimate for difference: -0.40
95% CI for difference: (-13.18, 12.38)
T-Test of difference = 0 (vs not =): T-Value = -0.07 P-Value = 0.948 DF = 18
Both use Pooled STD = 13.5978