Data Analysis On Academic Achievement Of Science Students

Task 1 (Boxplot and t tests)

Task 1 (Boxplot and t tests)

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1(a) The relevant boxplot is shown below.

The relevant five number summary is indicated below.

It is apparent from the shape of both the boxplots that the GPA distribution for neither of the genders is symmetric and hence there is skew involved. This is also confirmed from the fact that the presence of outliers on both ends for both genders since there are certain students who tend to perform very well and very miserably. Owing to the skewed nature of the data, the median in both cases is the appropriate measure of central tendency with IQR (Inter-quartile range) being the suitable measure for variation.

(b) The requisite hypotheses are as highlighted below.

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Null Hypothesis: Average GPA of males does not significantly deviate from average GPA of females

Alternative Hypothesis: Average GPA of males does significantly deviate from average GPA of females

Based on the alternative hypothesis, it is apparent that thee given test would be a two tail test. Also, the relevant test statistics would be T since the population standard deviation is not known for either of the two genders.  Further, the two samples are independent, hence 2 sample independent t test has been deployed whose excel output is highlighted as follows.

Two tail p value is 0.1972 which is greater than the level of significance (0.05). Hence, the available evidence is not sufficient to reject the null hypothesis and accept the alternative hypothesis. Therefore, no significant difference exists in the average GPA of the two genders.

2(a) The requisite hypotheses are as highlighted below.

Null Hypothesis: µPGUG which implies that no significant difference exists between the average GPA of students having post graduate parents and under graduate parents.

Alternate Hypothesis: µPGUG which implies that average GPA of students having post graduate parents is higher than the corresponding average GPA for students with under graduate parents.

Based on the alternative hypothesis, it is apparent that thee given test would be a one tail test. Also, the relevant test statistics would be T since the population standard deviation is not known for either of the two groups of students.  Further, the two samples are independent, hence 2 sample independent t test has been deployed whose excel output is highlighted as follows.

One tail p value is 0.1972 which is greater than the level of significance (0.05). Hence, the available evidence is not sufficient to reject the null hypothesis and accept the alternative hypothesis. Therefore, no significant difference exists in the average GPA of students with post graduate parents and under graduate parents.

(b) The requisite hypotheses are as highlighted below.

Null Hypothesis: µUGS which implies that no significant difference exists between the average GPA of students having under graduate parents and secondary & below qualification parents

Alternate Hypothesis: µUGS which implies that average GPA of students having under graduate parents is higher than the corresponding average GPA for students with secondary & below qualification parents.

Based on the alternative hypothesis, it is apparent that thee given test would be a one tail test. Also, the relevant test statistics would be T since the population standard deviation is not known for either of the two groups of students.  Further, the two samples are independent, hence 2 sample independent t test has been deployed whose excel output is highlighted as follows.

One tail p value is 0.000 which is lower than the level of significance (0.05). Hence, the available evidence is sufficient to reject the null hypothesis and accept the alternative hypothesis. Therefore, the average GPA of students with under graduate parents tends to exceed those students who have parents with secondary or less qualification.

3) The requisite correlation matrix is indicated below.

From the above, it is apparent that GPA has the highest correlation with the maths score at high school Next in line is the ATAR score which also has a correlation coefficient in excess of 0.4. The lowest correlation amongst the given factors is witnessed for English scores at high school.

4) (i) HS_SCI is a predictor of GPA considering that there is moderate correlation between the variables. It is also confirmed from the regression output where the slope of this variable is found to be significant.

(ii) HS_ENG is a predictor of GPA considering that there is moderate correlation between the variables. It is also confirmed from the regression output where the slope of this variable is found to be significant.

(iii) HS_MATH is a predictor of GPA considering that there is moderate correlation between the variables. It is also confirmed from the regression output where the slope of this variable is found to be significant.

(iv) ATAR is a predictor of GPA considering that there is moderate correlation between the variables. It is also confirmed from the regression output where the slope of this variable is found to be significant.

5) Step 1 output is indicated below.

Step 2 output is indicated below.

Step 3 output is indicated below.

Step 4 output is indicated below.

Step 5 output is indicated below.

Step 6 output is indicated below.

6) The output for step 5 is indicated below.

Interpretation of Slopes

HS_SCI – The slope of this implies that a unit change in the science score at high school would change the GPA of the student by 0.08. The direction of change in both variables would be same.

HS_ENG – The slope of this implies that a unit change in the English score at high school would change the GPA of the student by 0.04. The direction of change in both variables would be same.

HS_ MATH – The slope of this implies that a unit change in the Math score at high school would change the GPA of the student by 0.25. The direction of change in both variables would be same.

PARENT EDUC – The slope of this implies that a unit change in the parent highest education qualification would change the GPA of the student by 0.28. The direction of change in both variables would be same.

GENDER – For a female student, the GPA would be higher by 0.11 in comparison with a male student assuming all other factors are same.

Significance of Slopes

Null Hypothesis: The slope is not significant and can be assumed to be zero.

Alternative Hypothesis: The slope is significant and hence cannot be assumed to be zero.

The relevant test is a two tail test with the test statistics of choice being T. The respective values of the various t statistics coupled with the p values have already been estimated in the regression model as indicated below.

The decision rule is that the slope of a given variable would be considered significant only if the corresponding p value would be lower than 0.05 (significance level). Considering the p value of the various slope coefficients, it is apparent that the p value corresponding to two variables namely PARENT EDUC and HS_MATH is lower than 0.05. Hence, the slopes of PARENT EDUC and HS_MATH are significant while the other slopes are not significant.

7) The negative coefficient of ATAR in step 6 does surprise me since it would be expected that students have higher value of ATAR would have a higher GPA.  It is apparent that the p value corresponding to the slope of ATAR is 0.91 which is indicative of the fact that the slope of ATAR variable is not significant and can be assumed to be zero. Thus, it is apparent that the inclusion of ATAR does not improve the model fit and infact worsens the same which is apparent from the adjusted R square value.