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# 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

Model R R Square Adjusted R Square Std. Error of the Estimate
1 .786a .618 .617 5.30447

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

## Coefficientsa

Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) 14.577 1.658 8.789 .000
Tenth Grade Science Achievement .739 .029 .786 25.233 .000

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
Paired Differences t df Sig. (2-tailed)
Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference
Lower Upper
Pair 1 Attending in Zoom - Attending in Person -4.20000 4.93964 1.56205 -7.73360 -.66640 -2.689 9 .025
Paired Samples Correlations
N Correlation Sig.
Pair 1 Attending in Zoom & Attending in Person 10 .359 .308

### 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

N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum
Lower Bound Upper Bound
Northeast 80 58.9418 7.48700 .83707 57.2756 60.6079 34.36 70.42
North Central 100 55.6329 8.12019 .81202 54.0217 57.2441 34.88 70.18
South 144 56.2279 8.07886 .67324 54.8971 57.5587 35.48 70.69
West 75 58.1313 7.99595 .92329 56.2916 59.9710 36.57 71.05
Total 399 56.9807 8.03430 .40222 56.1900 57.7714 34.36 71.05

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

Levene Statistic df1 df2 Sig.
Twelfth Grade Math Achievement Based on Mean .707 3 395 .548
Based on Median .636 3 395 .592
Based on Median and with adjusted df .636 3 394.094 .592
Based on trimmed mean .752 3 395 .522

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.