Research Scenario 6.2: Work Status and Weekly Study Hours

Research Question

Do undergraduate students who work part-time jobs differ in weekly study hours compared to students who do not work?

Hypotheses

Null Hypothesis (H₀):
There is no difference in weekly study hours between students who work and students who do not work.

Alternative Hypothesis (H₁):
There is a difference in weekly study hours between students who work and students who do not work.

Install Required Packages

install.packages(“readxl”) install.packages(“ggpubr”) install.packages(“dplyr”) install.packages(“effectsize”) install.packages(“effsize”)

Open Packages

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

Dataset6_2 <- read_excel('/Users/sharathnallaganti/Desktop/3rd sem/applied analytics/Dataset6.2-2.xlsx')

Check Group Names

unique(Dataset6_2$Work_Status)
## [1] "Works"         "Does_Not_Work"

The dataset contains two independent groups: - “Works” - “Does_Not_Work”

These groups are independent because they consist of different students.

Descriptive Statistics

Dataset6_2 %>%
  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

Students who do not work: - Mean = 9.62 - Median = 8.54 - SD = 7.45 - N = 30

Students who work: - Mean = 6.41 - Median = 5.64 - SD = 4.41 - N = 30

On average, non-working students studied more hours per week.
However, the non-working group also shows greater variability (higher SD).

Create Vectors for Normality Testing

works_data <- na.omit(Dataset6_2$Study_Hours[Dataset6_2$Work_Status == "Works"])
nonworks_data <- na.omit(Dataset6_2$Study_Hours[Dataset6_2$Work_Status == "Does_Not_Work"])

Histograms (Normality Check)

hist(works_data,
     main = "Histogram of Study Hours (Works)",
     xlab = "Weekly Study Hours",
     col = "lightblue",
     border = "black",
     breaks = 10)

hist(nonworks_data,
     main = "Histogram of Study Hours (Does Not Work)",
     xlab = "Weekly Study Hours",
     col = "lightgreen",
     border = "black",
     breaks = 10)

Interpretation

Students who do not work show a wider spread of study hours, including some high values, indicating greater variability.

Students who work show a more concentrated distribution with fewer extreme values.

This suggests possible non-normality in the non-working group.

Boxplots (Outlier Check)

ggboxplot(Dataset6_2, 
          x = "Work_Status", 
          y = "Study_Hours",
          color = "Work_Status",
          palette = "jco",
          add = "jitter")

The non-working group displays more spread and potential extreme values.
The working group appears more compact.

Shapiro-Wilk Test of Normality

shapiro.test(works_data)
## 
##  Shapiro-Wilk normality test
## 
## data:  works_data
## W = 0.94582, p-value = 0.1305
shapiro.test(nonworks_data)
## 
##  Shapiro-Wilk normality test
## 
## data:  nonworks_data
## W = 0.83909, p-value = 0.0003695

Works group: W = 0.946, p = 0.131

Does_Not_Work group: W = 0.839, p = 0.00037

Because both groups must be normal for an Independent t-test, we cannot use a t-test.

Therefore, we proceed with the Mann-Whitney U test.

Mann-Whitney U Test

wilcox.test(Study_Hours ~ Work_Status, data = Dataset6_2)
## 
##  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

W = 569
p = 0.07973

Since p > .05, the difference is not statistically significant.

Statistical Conclusion

Students who work (Mdn = 5.64) were not significantly different from students who do not work (Mdn = 8.54) in weekly study hours,
U = 569, p > .05.

Although non-working students studied more on average (M = 9.62, SD = 7.45) than working students (M = 6.41, SD = 4.41), this difference was not statistically significant.

Final Interpretation

There is insufficient evidence to conclude that weekly study time differs between undergraduate students who work part-time and those who do not work.

While non-working students appear to study more hours on average, the observed difference may be due to random variation rather than a true difference between groups.