Statistical Analysis Assignment: Exploring Academic Performance and Geographic Factors

In this comprehensive statistical analysis assignment, we examine various facets of academic performance and their relationships. The first problem unveils a strong positive correlation between 10th and 12th-grade science achievements, providing insights into how early success can predict future outcomes. The second problem delves into the impact of different learning modalities (Zoom and in-person) on final exam scores, offering a glimpse into the evolving world of education. Lastly, we explore the influence of geographic location on 12th-grade math achievement, shedding light on regional disparities in academic performance. These analyses collectively provide valuable perspectives on educational and geographical factors affecting student success.

Problem Description

This assignment delves into three Statistical Analysis assignment. Firstly, it explores the strong positive correlation between 10th-grade and 12th-grade science achievement, utilizing a regression model. Secondly, it tests for a significant difference in final exam scores between in-person and Zoom class attendees. Finally, it investigates the influence of geographic location on 12th-grade math achievement using ANOVA. The results provide valuable insights into educational and geographical impacts on academic performance.

Problem 1:

Analysis of 10th and 12th Grade Science Achievement

In this problem, we conducted an analysis to determine the relationship between 10th-grade science achievement and 12th-grade science achievement. Here are the key findings:

Model Summary

Table 1: Predictors: (Constant), Tenth Grade Science Achievement

Coefficientsa

Table 2: Dependent Variable: Twelfth Grade Science Achievement

• Correlation: The correlation between the two variables is 0.786, indicating a strong positive correlation. This means that higher 10th-grade science achievement is associated with higher 12th-grade science achievement.
• Regression Equation: achsci12 = 14.577 + 0.739 * achsci10
• Coefficient of Determination: The coefficient of determination (R Square) is 0.618, indicating that 61.8% of the variability in the dependent variable (12th-grade science achievement) is explained by the model.
• Coefficient of Non-Determination:The coefficient of non-determination is 0.382, suggesting that 38.2% of the variation in the dependent variable is not explained by the model.

Fig 1:Scatterplot with fit line of 12th grade science achievement

Problem 2:

Comparison of Exam Scores for Zoom and In-Person Classes

This problem involves testing whether there is a significant difference in average scores on a final exam between students who attended classes on Zoom and students who attended classes in person.

Hypotheses:

• Null Hypothesis (H0):The average scores on the final exam are the same for both Zoom and in-person classes.
• Alternative Hypothesis (Ha): The average scores on the final exam differ between Zoom and in-person classes.

Paired Samples Test:

The t-test value is -2.689, and the correlation between Zoom and in-person class scores is 0.359.

Paired Samples Test Tables

Result:

The t-test for correlated samples revealed that attending in person produced significantly different average scores in the final exam (M=84.00) compared to students attending on Zoom (M=79.80). The t-statistic is -2.689, and the p-value is less than 0.05, indicating a significant difference.

Problem 3:

Impact of Geographic Location on 12th Grade Math Achievement

In this problem, we examined the impact of geographic location on 12th-grade math achievement. Here are the key findings:

Descriptive Statistics: The mean, standard deviation, and other statistics for 12th-grade math achievement are provided for different geographic regions.

Descriptives

Twelfth Grade Math Achievement

Table 4: Descriptive statistics- Results of SPSS

Test of Homogeneity of Variances: The test indicates that there is homogeneity of variance among the groups.

Test of Homogeneity of Variances

Table 5: Test of Homogeneity of Variances

ANOVA:An analysis of variance (ANOVA) was performed, showing that there is a significant impact of geographic location on 12th-grade math achievement.

ANOVA

Twelfth Grade Math Achievement

Table 6: ANOVA Results

Conclusion:Students from different geographic regions have varying levels of math achievement, with the Northeast region having the highest mean score and the North Central region having the lowest. The one-way ANOVA test confirms that these differences are statistically significant.