Assignment

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## 1. Problem Statement

Swiss transport planners want to determine whether people use the tram more frequently than the Bus Rapid Transit (BRT). Understanding this difference helps guide infrastructure investment and sustainable transport policy decisions.

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## 2. Hypotheses

- **Null Hypothesis (H₀):** There is no difference in average daily trips between tram and BRT users.
- **Alternative Hypothesis (H₁):** Tram users make more daily trips than BRT users.

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## 3. Description of the Data

The dataset contains daily trips per person for two independent groups:

- 7 tram users
- 7 BRT users
- Outcome variable: number of trips per day (numeric)

```{r}
# Create sample data
tram <- c(5, 6, 5, 8, 7, 6, 4)
brt <- c(4, 3, 5, 4, 3, 4, 6)

length(tram)
length(brt)

## Description of the Data

Sample data of daily trips per person:

| Mode | Trips per person |
|——|—————-|
| Tram | 5, 6, 5, 8, 7, 6, 4 |
| BRT | 4, 3, 5, 4, 3, 4, 6 |

- **Variable:** `trips` (numeric)
- **Groups:** `mode` (tram, BRT)
- **Sample size:** 7 for each mode

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## Justification of the Chosen Test

- Two independent groups (tram vs BRT)
- Numeric outcome variable (`trips`)
- **Two-sample t-test** is appropriate to compare means
- Assumptions:
- Approximately normally distributed (Shapiro-Wilk test)
- Equal variance (var.equal = TRUE)
- If assumptions fail → non-parametric alternative: Mann-Whitney U test

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## R Code Implementation

```{r}
# Load necessary package for effect size (optional)
# install.packages(“effsize”) # Run only if not installed
library(effsize)

# Create the sample data
tram <- c(5, 6, 5, 8, 7, 6, 4)
brt <- c(4, 3, 5, 4, 3, 4, 6)

# Check normality assumption
shapiro.test(tram) # p > 0.05 → approximately normal
shapiro.test(brt) # p > 0.05 → approximately normal

# Conduct two-sample t-test (tram > BRT)
t_test_result <- t.test(tram, brt, alternative = “greater”, var.equal = TRUE)
t_test_result

# Calculate group means
mean(tram)
mean(brt)

# Calculate effect size (Cohen’s d) manually
mean_tram <- mean(tram)
mean_brt <- mean(brt)

sd_pooled <- sqrt(((length(tram)-1)*var(tram) +
(length(brt)-1)*var(brt)) /
(length(tram)+length(brt)-2))

cohens_d <- (mean_tram - mean_brt) / sd_pooled
cohens_d