# Statistical Analysis Assignment: Exploring Academic Performance and Geographic Factors

September 15, 2023
Zoey Moore
🇺🇸 United States
Statistics
Zoey Moore is a seasoned Statistics Coursework Helper with 12 years of experience. She holds a master's degree from the University of Pennsylvania, USA. Zoey is a trusted guide for students seeking assistance with their assignments.
Key Topics
• Problem Description
• Problem 1:
• Model Summary
• Coefficientsa
• Problem 2:
• Hypotheses:
• Paired Samples Test:
• Paired Samples Test Tables
• Problem 3:
• Descriptives
• Test of Homogeneity of Variances
• ANOVA

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

ModelRR SquareAdjusted R SquareStd. Error of the Estimate
1.786a.618.6175.30447

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

## Coefficientsa

ModelUnstandardized CoefficientsStandardized CoefficientstSig.
BStd. ErrorBeta
1(Constant)14.5771.6588.789.000

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 DifferencestdfSig. (2-tailed)
MeanStd. DeviationStd. Error Mean95% Confidence Interval of the Difference
LowerUpper
Pair 1Attending in Zoom - Attending in Person-4.200004.939641.56205-7.73360-.66640-2.6899.025
Paired Samples Correlations
NCorrelationSig.
Pair 1Attending in Zoom & Attending in Person10.359.308

### 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

NMeanStd. DeviationStd. Error95% Confidence Interval for MeanMinimumMaximum
Lower BoundUpper Bound
Northeast8058.94187.48700.8370757.275660.607934.3670.42
North Central10055.63298.12019.8120254.021757.244134.8870.18
South14456.22798.07886.6732454.897157.558735.4870.69
West7558.13137.99595.9232956.291659.971036.5771.05
Total39956.98078.03430.4022256.190057.771434.3671.05

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 Statisticdf1df2Sig.
Twelfth Grade Math AchievementBased on Mean.7073395.548
Based on Median.6363395.592
Based on Median and with adjusted df.6363394.094.592
Based on trimmed mean.7523395.522

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.