Research Question 1: Study Hours and Exam Scores

Part 1: Descriptive Statistics (Dataset A)

DatasetA <- read_excel("/Users/asfia/Desktop/DatasetA.xlsx")
mean(DatasetA$StudyHours); sd(DatasetA$StudyHours)
## [1] 6.135609
## [1] 1.369224
mean(DatasetA$ExamScore); sd(DatasetA$ExamScore)
## [1] 90.06906
## [1] 6.795224

Interpretation: For Research Question 1, the Independent Variable is Study Hours and the Dependent Variable is Exam Score. The average study time was approximately 5 hours (\(M = 4.97, SD = 1.37\)), while the average exam score was 90% (\(M = 90.07, SD = 6.80\)).

Part 2 & 3: Check Normality & Shapiro-Wilk (Dataset A)

shapiro.test(DatasetA$StudyHours)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetA$StudyHours
## W = 0.99388, p-value = 0.9349
shapiro.test(DatasetA$ExamScore)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetA$ExamScore
## W = 0.96286, p-value = 0.006465
hist(DatasetA$StudyHours, main="Histogram of Study Hours", col="lightblue", breaks=20)

hist(DatasetA$ExamScore, main="Histogram of Exam Scores", col="lightgreen", breaks=20)

Interpretation: We used Shapiro-Wilk tests and Histograms to check for normality. While Study Hours was normal, the Exam Score failed the normality test (\(p = 0.006\)) and the histogram shows a left-skewed distribution. Because one variable is not normal, we must use the Spearman Rank Correlation.

Part 4 & 5: Correlation and Scatterplot (Dataset A)

cor.test(DatasetA$StudyHours, DatasetA$ExamScore, method = "spearman")
## Warning in cor.test.default(DatasetA$StudyHours, DatasetA$ExamScore, method =
## "spearman"): Cannot compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  DatasetA$StudyHours and DatasetA$ExamScore
## S = 16518, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.9008825
ggscatter(DatasetA, x = "StudyHours", y = "ExamScore", add = "reg.line", 
          xlab = "Study Hours", ylab = "Exam Score", title = "Study vs Exam")

Interpretation: There is a strong positive correlation (\(\rho = 0.90, p < 0.001\)) between study hours and exam scores. The scatterplot shows a clear upward trend with a tight fit to the regression line, indicating that more study time leads to higher scores.

Research Question 2: Phone Use and Sleep

Part 1: Descriptive Statistics (Dataset B)

DatasetB <- read_excel("/Users/asfia/Desktop/DatasetB.xlsx")
mean(DatasetB$ScreenTime); sd(DatasetB$ScreenTime)
## [1] 5.063296
## [1] 2.056833
mean(DatasetB$SleepingHours); sd(DatasetB$SleepingHours)
## [1] 6.938459
## [1] 1.351332

Interpretation: For Research Question 2, the Independent Variable is Screen Time and the Dependent Variable is Sleeping Hours. Average daily screen time was 5 hours (\(M = 5.06, SD = 2.06\)), with an average of 7 hours of sleep (\(M = 6.94, SD = 1.35\)).

Part 2 & 3: Check Normality & Shapiro-Wilk (Dataset B)

shapiro.test(DatasetB$ScreenTime)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetB$ScreenTime
## W = 0.90278, p-value = 1.914e-06
shapiro.test(DatasetB$SleepingHours)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetB$SleepingHours
## W = 0.98467, p-value = 0.3004
hist(DatasetB$ScreenTime, main="Histogram of Screen Time", col="pink", breaks=20)

hist(DatasetB$SleepingHours, main="Histogram of Sleeping Hours", col="lightyellow", breaks=20)

Interpretation: The Screen Time variable failed the normality test significantly (\(p < 0.001\)) and its histogram is right-skewed. Because this variable is not normally distributed, the Spearman Rank Correlation is the appropriate method.

Part 4 & 5: Correlation and Scatterplot (Dataset B)

cor.test(DatasetB$ScreenTime, DatasetB$SleepingHours, method = "spearman")
## 
##  Spearman's rank correlation rho
## 
## data:  DatasetB$ScreenTime and DatasetB$SleepingHours
## S = 259052, p-value = 3.521e-09
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.5544674
ggscatter(DatasetB, x = "ScreenTime", y = "SleepingHours", add = "reg.line", 
          xlab = "Screen Time", ylab = "Sleeping Hours", title = "Phone vs Sleep")

Interpretation: There is a moderate negative correlation (\(\rho = -0.55, p < 0.001\)) between screen time and sleep. The downward trend in the scatterplot shows that as phone usage increases, total sleep hours tend to decrease.

Part 6: Final Results Summary