Assignment 3

Getting to know the data:

Hypotheses:

Correlation hypotheses:

## 
##  Pearson's product-moment correlation
## 
## data:  data$wage and data$distance
## t = -0.026872, df = 4737, p-value = 0.9786
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.02886256  0.02808233
## sample estimates:
##           cor 
## -0.0003904288

## 
##  Pearson's product-moment correlation
## 
## data:  data$education and data$distance
## t = -6.4414, df = 4737, p-value = 1.301e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.12133362 -0.06488278
## sample estimates:
##         cor 
## -0.09318309

## 
##  Pearson's product-moment correlation
## 
## data:  data$tuition and data$distance
## t = -6.9858, df = 4737, p-value = 3.226e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1290819 -0.0727172
## sample estimates:
##        cor 
## -0.1009806

interpretation:

According to the results, there’s no strong enough evidence, to support the hypothesis of significant correlation between \(wage\) and \(distance\) (\(r=-.0004, p>.05\)), However, there’s a strong enough evidence to support significance correlation between \(education\) and \(distance\) (\(r=-.0932, p<.001\)), and \(tuition\) and \(distance\) (\(r=-0.1010, p<.001\)). Nonetheless, in all 3 cases, Pearson Correlation indicates a low level of correlation (all negative, approximating 0) between all the variables.

Results and interpretation:

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value   Pr(>F)    
## group    2  25.638 8.42e-12 ***
##       4736                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##  Two Sample t-test
## 
## data:  distance by gender
## t = 0.23683, df = 4737, p-value = 0.8128
## alternative hypothesis: true difference in means between group female and group male is not equal to 0
## 95 percent confidence interval:
##  -0.1155914  0.1473560
## sample estimates:
## mean in group female   mean in group male 
##             1.810038             1.794156

## 
##  Welch Two Sample t-test
## 
## data:  distance by urban
## t = 34.944, df = 4587.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group no and group yes is not equal to 0
## 95 percent confidence interval:
##  1.483114 1.659422
## sample estimates:
##  mean in group no mean in group yes 
##         2.1689133         0.5976449

## 
##  Kruskal-Wallis rank sum test
## 
## data:  distance by ethnicity
## Kruskal-Wallis chi-squared = 104.18, df = 2, p-value < 2.2e-16

interpretation:

According to Levene’s test, there’s a significance difference between the groups’ variances (\(F(2,4736)=25.638, p<.001\)). As for the results, there’s no significant difference between genders (\(t(4737)=0.237, p>.05\)), but there is significant differences between urban / non-urban respondents (\(t(4587.8)=34.944, p<.001\)). As for the Kruskal-Wallis test, according to the results, there’s a strong enough evidence to reject the null hypothesis, and support the alternative hypothesis (\(\chi^2_2=104.18, p<.001\)).

* * *

Descriptive Statistics:

Scatter plots:

interpretation:

It seems there’s no specific pattern for the correlation between the distance to college, and either wage, or years of education or level of tuition.

Box plots:

interpretation:

As for distance by Gender, it seems there’s no substantial difference between males and females in the distance they live from their college. As for students that live in urban area and students who don’t, the distance for students that live out of urban area, is noticeably greater than for students who don’t. As for ethnicity, there’s no meaningful differences in the distance they have for their college.