Question 2: Sleep vs. Phone Usage

# Load data
q2 <- read_excel("A4Q2.xlsx")
head(q2)
## # A tibble: 6 × 2
##   sleep  phone
##   <dbl>  <dbl>
## 1  9.03  1.78 
## 2  6.76  6.62 
## 3  9.18  0.289
## 4  7.20  3.33 
## 5  3    10    
## 6  6.71  4.24
str(q2)
## tibble [150 × 2] (S3: tbl_df/tbl/data.frame)
##  $ sleep: num [1:150] 9.03 6.76 9.18 7.2 3 ...
##  $ phone: num [1:150] 1.784 6.624 0.289 3.325 10 ...
summary(q2)
##      sleep            phone        
##  Min.   : 2.000   Min.   : 0.2608  
##  1st Qu.: 6.931   1st Qu.: 1.9057  
##  Median : 7.524   Median : 3.2708  
##  Mean   : 7.559   Mean   : 3.8046  
##  3rd Qu.: 8.372   3rd Qu.: 4.8773  
##  Max.   :10.089   Max.   :15.0000
# Test for normality
shapiro.test(q2$sleep)
## 
##  Shapiro-Wilk normality test
## 
## data:  q2$sleep
## W = 0.91407, p-value = 8.964e-08
shapiro.test(q2$phone)
## 
##  Shapiro-Wilk normality test
## 
## data:  q2$phone
## W = 0.89755, p-value = 9.641e-09

Normality Assessment:
A Shapiro-Wilk normality test was conducted for both variables. Sleep (\(p < 0.001\)) and phone usage (\(p < 0.001\)) were not normally distributed (\(p < 0.05\)). Therefore, the Spearman correlation test was selected.

# Spearman Correlation
cor.test(q2$phone, q2$sleep, method = "spearman")
## 
##  Spearman's rank correlation rho
## 
## data:  q2$phone and q2$sleep
## S = 908390, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.6149873

Interpretation:
A Spearman correlation test was conducted to examine the relationship between hours of sleep and hours of phone use. There was a moderate negative correlation between sleep and phone use (\(\rho = -0.615, p < 0.001\)). This indicates that people who spend more time using their phones tend to sleep fewer hours, and the relationship is statistically significant.