#Question 1: Age vs. Education

# Load data
q1 <- read_excel("A4Q1.xlsx")
head(q1)
## # A tibble: 6 × 2
##     age education
##   <dbl>     <dbl>
## 1  42.0      13.2
## 2  38.0      12.6
## 3  16.4      10.3
## 4  33.8      16.2
## 5  33.4      14.0
## 6  14.3      11.4
str(q1)
## tibble [150 × 2] (S3: tbl_df/tbl/data.frame)
##  $ age      : num [1:150] 42 38 16.4 33.8 33.4 ...
##  $ education: num [1:150] 13.2 12.6 10.3 16.2 14 ...
summary(q1)
##       age           education     
##  Min.   : 8.657   Min.   : 6.196  
##  1st Qu.:27.887   1st Qu.:12.024  
##  Median :35.798   Median :14.029  
##  Mean   :35.326   Mean   :13.827  
##  3rd Qu.:42.549   3rd Qu.:15.851  
##  Max.   :62.923   Max.   :19.727
# Test for normality
shapiro.test(q1$age)
## 
##  Shapiro-Wilk normality test
## 
## data:  q1$age
## W = 0.99194, p-value = 0.5581
shapiro.test(q1$education)
## 
##  Shapiro-Wilk normality test
## 
## data:  q1$education
## W = 0.9908, p-value = 0.4385

Normality Assessment:
A Shapiro-Wilk normality test was conducted for both variables. Age (\(p = 0.5581\)) and education (\(p = 0.4385\)) were both normally distributed (\(p > 0.05\)). Therefore, the Pearson correlation test was selected.

# Pearson Correlation
cor.test(q1$age, q1$education, method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  q1$age and q1$education
## t = 7.4066, df = 148, p-value = 9.113e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3924728 0.6279534
## sample estimates:
##       cor 
## 0.5200256

Interpretation:
A Pearson correlation test was conducted to examine the relationship between age and years of education. There was a moderate positive correlation between age and years of education (\(r = 0.520, p < 0.001\)). This indicates that as age increases, years of education tend to increase, and the relationship is statistically significant.