Difference in Overall Marks - Essay Example

The paper "Difference in Overall Marks " is an outstanding example of a statistics essay. In general, the overall mark of On-campus students is believed to be higher than that of distance students. This is because on-campus students are assumed to have more ample time to study without interference. However, with the emergence of online e-learning, the performance of on-campus and distance students is believed to be almost similar. To evaluate the performance of on-campus and distance students, the overall marks for STATS 101 of the on-campus and distance students can be compared.

Figure 2.4 illustrates the box plots of the overall mark of STATS 101 for on-campus and distance students.

Figure 2.4

The box plots in figure 2.4 above indicate that the overall marks of distance students tend to be higher than that of on-campus students.

Table 2.4 illustrates the Excel output of the two tail z-test to test if the overall mark for distance students is the same as that of on-campus students.

Table 2.4

The p-value of the test is 0.1394, therefore it can be concluded that whereas some distance students have higher overall marks than on-campus students, the overall marks of both distance and on-campus students do not differ significantly.

2.5 Relationship between assignment and examination marks

Generally, the performance of most students in assignments and subsequently in the examination is almost similar. This section evaluates the relationship between the assignment and examination marks of students in STATS 101. In the model to be evaluated, examination marks will be predicted using the assignment marks.

Figure 2.5 shows the scatter plot of the examination marks against the assignment marks of students in STATS 101. The scatter plot illustrates that students with higher marks in the assignment also tend to have higher marks in the examination. Also included in the scatter plot is the regression equation with assignment marks as the independent variable and examination marks as the dependent variable. The equation can be written as follows;

Examination marks = 8.824 + 0.756 x (Assignment marks)

Figure 2.5

The slope of the equation 0.756 indicates that for each additional mark in the assignment, the mean examination mark is expected to increase by about 0.756 marks. On the other hand, the constant in the regression equation indicates the examination mark of a student who gets zero in the assignment. Therefore, in STATS 101, a student who gets a zero in the assignment will manage to get approximately 8.824 marks in the examination.

The excel output in table 2.5 shows the strength of the relationship between the assignment and examination marks of students in STATS 101.

Table 2.5

As illustrated by the scatter plot, the correlation coefficient of 0.683 is positive. The correlation coefficient is relatively high which shows a relatively strong relationship between the assignment and examination marks of students in STATS 101. In addition, the coefficient of determination 0.466 shows that 46.6% of the variation in the examination marks is explained by the variation in the assignment marks. This indicates that there are other factors that explain the larger proportion of the variation in examination marks.

2.6 Relationship between assignment and examination marks with the number of online tests attempted included

The number of online tests attempted by a student tends to improve the marks of the students in the examination. Therefore, adding the number of online tests attempted as the second independent variable could improve the model used for predicting the examination mark of a student in STATS 101.

Table 2.6 shows the excel output of the regression model established. The regression equation can be written as follows;

Examination marks = -1.523 + 0.579 x (Assignment marks) + 6.731 x (Number of online tests attempted)

The slopes in the regression equation 0.579 and 6.731 Indicate that for each additional mark in the assignment, the mean examination mark is expected to increase by about 0.579 marks, while every additional online test attempted is expected to increase the mean examination mark by 6.731 marks.

The multiple correlation coefficient 0.743, is higher and closer to 1 than 0.683. This shows that adding the number of online tests attempted to the model makes it stronger. In addition, the coefficient of determination 0.552 further shows that the second independent variable strengthens the model. Therefore, 55.2% of the variation in the examination marks is explained jointly by the variation in the assignment marks and the number of online tests attempted.