Inferential Statistics – Two-Sample t-test

R progrmming

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# Inferential Statistics – Two-Sample Hypothesis Testing
# Male vs Female Results  |  R Programming (Professional Style)
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# 1) Define the two independent samples
male   <- c(97,96,88,80,90,84,79,92,96,70,85,77)      # Male scores
female <- c(99,94,92,75,96,88,87,98,95,72,83,79)      # Female scores

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# 2) Descriptive Statistics
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mean(male);   sd(male)      # Mean & SD for male group

## [1] 86.16667

## [1] 8.54755

mean(female); sd(female)    # Mean & SD for female group

## [1] 88.16667

## [1] 9.133687

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# 3) Two-Sample t-Test
# H0: mean(male) = mean(female)
# H1: mean(male) ≠ mean(female)
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test_result <- t.test(male, female, var.equal = FALSE)
test_result

## 
##  Welch Two Sample t-test
## 
## data:  male and female
## t = -0.55384, df = 21.904, p-value = 0.5853
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -9.490972  5.490972
## sample estimates:
## mean of x mean of y 
##  86.16667  88.16667

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# 4) Professional Visualization (LinkedIn style)
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# Create boxplot
boxplot(male, female,
        names = c("Male","Female"),
        main  = "Two-Sample Hypothesis Testing (R)",
        ylab  = "Exam Scores",
        border = "black")

# Add mean lines for clarity
abline(h = mean(male),   lty = 2)   # Male mean line
abline(h = mean(female), lty = 3)   # Female mean line

# Add mean points
points(1, mean(male),   pch = 19)
points(2, mean(female), pch = 19)

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# 5) Quick Interpretation (optional for teaching videos)
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# If p-value < 0.05 → Significant difference between groups
# If p-value ≥ 0.05 → No significant difference