Car Fuel Efficiency: Transmission Type and Fuel Type
Analysis
Utsav Sapkota
April 2025
Abstract
This project investigates the impact of transmission type and fuel type on vehicle
fuel efficiency. Using a dataset of 234 cars, I conduct hypothesis tests to determine
whether manual transmission vehicles achieve higher highway mileage than automatic
vehicles and whether manual transmission cars outperform a standard benchmark of 23
miles per gallon. Both mathematical model tests and randomization tests are applied
to reach conclusions based on real-world data.
Introduction
Fuel efficiency is a key consideration for consumers and policymakers alike. Advances in
automotive technology have blurred the lines between automatic and manual transmission
efficiency (Edmunds, 2022; Deaton, n.d.). Nevertheless, questions persist regarding whether
manual vehicles maintain an edge, particularly in highway driving conditions. Additionally,
fuel type —gasoline, diesel, or ethanol —plays an important role in determining overall
performance (Car and Driver, 2025; SpringerNature, 2015).
Personally, I have always been intrigued by how data can reveal patterns in everyday
decisions—like choosing a car. This topic felt relevant not just as a statistical study, but as
a way to connect real-world consumer behavior to data-driven conclusions.
This study addresses two research questions:
1. Is there a statistically significant difference in average highway mileage between manual
and automatic transmission vehicles?
1
2. Do manual transmission vehicles demonstrate superior highway mileage compared to
an expected benchmark of 23 miles per gallon?
Hypothesis Test 1: Difference in Means (Manual vs Automatic)
Part A
Research Question: Is there a statistically significant difference in average highway mileage
between manual and automatic cars?
Variables:
• Transmission Type (Categorical: automatic or manual)
• Highway Mileage (Numerical: miles per gallon)
Hypotheses:
• H0 : µauto = µmanual
• HA : µauto ̸= µmanual
Significance Level: α = 0.05
Part B – Mathematical Model Hypothesis Test
Sample statistics:
• Automatic: n1 = 51, x̄1 = 21.43, s1 = 4.77
• Manual: n2 = 13, x̄2 = 24.54, s2 = 4.35
Standard Error (SE):
s
SE =
s21
s2
+ 2 =
n1 n2
r
22.76 18.92
+
≈ 1.38
51
13
Test Statistic (t):
t=
x̄1 − x̄2
21.43 − 24.54
=
≈ −2.25
SE
1.38
2
Degrees of Freedom: df = min(n1 − 1, n2 − 1) = 12
P-Value: Using the t-distribution, p ≈ 0.045.
Conclusion: Since p < 0.05, we reject the null hypothesis. There is statistically significant evidence that manual cars have different average highway mileage compared to automatic cars.
Because we are comparing the means of two independent samples (manual vs. automatic),
a two-sample t-test is appropriate here. Although the sample sizes are unequal, the test
remains valid due to the use of standard error and degrees of freedom adjustment.
Figure 1: Boxplot Comparing Highway Mileage for Automatic and Manual Transmission
Cars
Figure 1 visually supports this difference, showing a clear upward shift in the highway
mileage distribution for manual cars.
Part C – Randomization Hypothesis Test
A randomization hypothesis test was conducted in StatKey using 1,000 resamples.
Observed Difference:
x̄auto − x̄manual = −3.11
P-Value:
p ≈ 0.038
3
Conclusion: Since p < 0.05, we again reject the null hypothesis, supporting the conclusion that transmission type affects highway fuel efficiency.
Figure 2: Randomization distribution from StatKey for the difference in means. The observed difference of 1.706 lies in the right tail, with an estimated p-value of 0.025 based on
1,000 resamples. This supports rejecting the null hypothesis that µ1 = µ2 .
Part D – Synthesis
Both the mathematical model and the randomization method produced p-values below 0.05,
leading to the same conclusion. Manual transmission vehicles, on average, outperform automatic vehicles in terms of highway fuel efficiency within this sample. Given the slight
imbalance in sample sizes, the randomization test provides a robust and reliable result.
Hypothesis Test 2: Single Mean (Manual vs Benchmark)
Part A – Setup
Research Question: Do manual transmission cars achieve greater average highway mileage
than 23 mpg?
Hypotheses:
• H0 : µ = 23
4
• HA : µ > 23
Significance Level: α = 0.05
Part B – Mathematical Model Hypothesis Test
Sample statistics:
• n = 13
• x̄ = 24.54
• s = 4.35
Standard Error (SE):
s
4.35
SE = √ = √ ≈ 1.207
n
13
Test Statistic (t):
t=
24.54 − 23
x̄ − 23
=
≈ 1.28
SE
1.207
P-Value: Using the t-distribution with 12 degrees of freedom, p ≈ 0.111.
Conclusion: Since p > 0.05, we fail to reject the null hypothesis. There is not enough
evidence to conclude that manual cars achieve greater than 23 mpg on average.
Since this test compares a sample mean to a fixed benchmark, a one-sample t-test is
appropriate. The sample size is relatively small, but the test is robust under the assumption
of approximate normality.
Part C – Randomization Hypothesis Test
A randomization test conducted in StatKey yielded a similar p-value of approximately p =
0.10, confirming the result from the mathematical model.
Part D – Synthesis
Both methods agree that there is insufficient statistical evidence to conclude that manual
cars exceed an average highway mileage of 23 mpg. Although the sample mean was higher,
variability and small sample size limited the strength of the result.
5
Confidence Interval: Difference in Means
To further investigate the difference in average highway mileage between automatic and
manual transmission cars, I constructed a 95% confidence interval for the difference in means.
Mathematical Model Confidence Interval
Using the sample statistics:
• x̄manual = 24.54, s2 = 4.35, n2 = 13
• x̄auto = 21.43, s1 = 4.77, n1 = 51
We calculate:
r
SE =
4.772 4.352
+
≈ 1.38
51
13
t∗ ≈ 2.179 (from t-distribution with df = 12, 95%)
CI = (24.54 − 21.43) ± 2.179 × 1.38 = 3.11 ± 3.01 = (0.10, 6.12)
Interpretation
We are 95% confident that the true difference in average highway mileage (manual - automatic) is between 0.10 and 6.12 mpg. Because the interval does not contain 0, this supports
the hypothesis that manual cars tend to have higher highway mileage. This reinforces the
conclusion drawn in Hypothesis Test 1.
Final Conclusion
The analysis of transmission types and fuel efficiency reveals that transmission choice significantly impacts highway mileage. Manual cars in this dataset perform better than automatic
cars, aligning with earlier studies suggesting that manual transmissions often provide fuel
economy advantages under certain conditions. However, when compared to an absolute
benchmark (23 mpg), the evidence is not strong enough to conclude superiority at the 5%
significance level.
This project also demonstrates how combining classical inference with randomizationbased methods strengthens our understanding, especially when working with real-world
datasets that are noisy, small, or imbalanced.
6
References
• Car and Driver. (2025). E85 fuel explained: Everything you need to know. Retrieved
from https://www.caranddriver.com/features/a64255534/e85-fuel-explained/
• Deaton, J. P. (n.d.). Are manual transmission cars more efficient than automatics?
HowStuffWorks. Retrieved from https://auto.howstuffworks.com/fuel-efficiency/fueleconomy/manual-transmission-cars-more-efficient-than-automatics.htm
• Edmunds. (2022). Five myths about stick shifts. Retrieved from https://www.edmunds.com/fueleconomy/five-myths-about-stick-shifts.html
• SpringerNature. (2015). Life cycle assessment of gasoline and diesel fuel. Retrieved
from https://link.springer.com/article/10.1007/s10098-014-0793-9
7