This report takes a look into whether taking a preparation course helps students perfom better.A fictional data set by Royce Kimmons was used which includes scores for three exams and a variety of personal, social, and economic factors that have interaction effects upon them. The scores used in this report are math and reading scores, and other factors include gender and parental level of education.

The graph above shows the ratio of people who took the test prepation for both genders.It shows that a higher number of the both male and females did not complete the test preparation course.

In this report \(\mu_1\) denotes the population mean for students who did not complete the prep test course whilst \(\mu_2\) denotes the population mean for students who completed the prep test course.

The figure above shows grade distributions for students who completed and did not complete the test preparation course.The density curve of those who did not take the test is more distributed to the left whereas the curve of the students who completed the preparation test is mostly distributed to the right. The difference in side that the curves are distributed show that more population mean for those who did not complete the test is less than the mean of those who did take the preparation course.

To further investigate and provide evidence whether the prep course is effective a two-sample hypothesis test was perfomed at 0.05 level of significance.The following null hypothesis and alternative hypothesis were used

\[H_0 :\mu_1 =\mu_2\] \[H_a :\mu_1 < \mu_2 \]

The test results gave a p-value equal to 1.043e-08, close to zero and the null was rejected. The test proved that the sample mean for the students who did not take the prep course, \(\bar{x}_1\) = 64 is less than the sample mean of the students who completed the prep course, \(\bar{x}_2\) =70. At 0.05 level of significance there is enough evidence to prove that completing the prep test is effective.

For further testing a look into the reading score distribution was done and the probability density curves had the same outcome as the math score distribution, proving that the grades did not only improve for math as a subject but completing a preparation course for any subject helps get better grades.

The graph above shows the parental level of education for students within the sample. The graph shows how a larger number of parents under every level of education did not have their child complete the preparation course. This proves that chances of having a student complete the test was to a lesser extend influenced by the parental level of education. Educating the students and the parents on the effectiveness of completing a preparation course would result in more students completing the prep course.

Reference:

Kimmons, Royce. “Understanding Digital Participation Divides.” Exam Scores, http://roycekimmons.com/tools/generated_data/exams.

Disclaimer:

All data set is are fictional. These results are not suitable for research purposes.