RQ-2

Import Library

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(effectsize)
library(effsize)

Import dataset

data <- read_excel("C:/Users/Admin/Downloads/Dataset6.2-2.xlsx")

Check data

head(data)

## # A tibble: 6 × 2
##   Work_Status Study_Hours
##   <chr>             <dbl>
## 1 Works             3.57 
## 2 Works            13.2  
## 3 Works             0.577
## 4 Works             6.65 
## 5 Works            17.3  
## 6 Works             8.47

str(data)

## tibble [60 × 2] (S3: tbl_df/tbl/data.frame)
##  $ Work_Status: chr [1:60] "Works" "Works" "Works" "Works" ...
##  $ Study_Hours: num [1:60] 3.568 13.247 0.577 6.65 17.344 ...

Descriptive statistics

data %>%
  group_by(Work_Status) %>%
  summarise(
    Mean = mean(Study_Hours, na.rm = TRUE),
    Median = median(Study_Hours, na.rm = TRUE),
    SD = sd(Study_Hours, na.rm = TRUE),
    N = n()
  )

## # A tibble: 2 × 5
##   Work_Status    Mean Median    SD     N
##   <chr>         <dbl>  <dbl> <dbl> <int>
## 1 Does_Not_Work  9.62   8.54  7.45    30
## 2 Works          6.41   5.64  4.41    30

Histogram

hist(data$Study_Hours[data$Work_Status=="Works"],
     main = "Histogram of Study Hours (Works)",
     xlab = "Study Hours",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

The histogram for the Works group appears moderately symmetric with no extreme skew. The distribution does not show clear deviations from normality.

hist(data$Study_Hours[data$Work_Status=="Does_Not_Work"],
     main = "Histogram of Study Hours (Does Not Work)",
     xlab = "Study Hours",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

The histogram for the Does_Not_Work group appears visibly skewed with several values extending further on one side, suggesting the data may not be normally distributed.

Boxplot

ggboxplot(data,
          x = "Work_Status",
          y = "Study_Hours",
          color = "Work_Status",
          add = "jitter")

The Works boxplot appears mostly normal. There are no extreme outliers beyond the whiskers. The Does_Not_Work boxplot appears less symmetric, with greater spread and some points further from the central distribution, suggesting potential non-normality.

Shapiro-Wilk normality tests

shapiro.test(data$Study_Hours[data$Work_Status=="Works"])

## 
##  Shapiro-Wilk normality test
## 
## data:  data$Study_Hours[data$Work_Status == "Works"]
## W = 0.94582, p-value = 0.1305

shapiro.test(data$Study_Hours[data$Work_Status=="Does_Not_Work"])

## 
##  Shapiro-Wilk normality test
## 
## data:  data$Study_Hours[data$Work_Status == "Does_Not_Work"]
## W = 0.83909, p-value = 0.0003695

The Shapiro–Wilk test for the Works group was not significant (p > .05). This means the data is normally distributed. The Shapiro–Wilk test for the Does_Not_Work group was significant (p < .05). This means the data is not normally distributed.Since one group is not normal, we cannot use the independent t-test.

Mann–Whitney U test (Wilcoxon Rank Sum)

wilcox.test(Study_Hours ~ Work_Status, data = data)

## 
##  Wilcoxon rank sum exact test
## 
## data:  Study_Hours by Work_Status
## W = 569, p-value = 0.07973
## alternative hypothesis: true location shift is not equal to 0

The Mann–Whitney U test was not statistically significant (p > .05).This means there is no significant difference in Study Hours between students who work and students who do not work.

Interpretation

Working Students Group ((Mdn = 5.64) was not significantly different from Non-Working Students Group (Mdn = 8.54), U = 569, p = .07973. The data wasn’t Statically Significant