Overview

This project will attempt to see if there is a relationship between the distance a punt travels and the type of air used to inflate the ball.

Introduction

Two identical footballs, one air-filled and one helium-filled, were used outdoors on a windless day at The Ohio State University’s athletic complex. Each football was kicked 39 times and the two footballs were alternated with each kick. The experimenter recorded the distance traveled by each ball. This data was obtained through openintro, with credit to Lafferty, M.B. Courtesy of the Columbus Dispatch, November 21 1993.

Exploring the Data

library(openintro)
## Please visit openintro.org for free statistics materials
## 
## Attaching package: 'openintro'
## The following objects are masked from 'package:datasets':
## 
##     cars, trees
helium<- helium
summary(helium)
##      trial           air            helium     
##  Min.   : 1.0   Min.   :15.00   Min.   :11.00  
##  1st Qu.:10.5   1st Qu.:23.50   1st Qu.:24.50  
##  Median :20.0   Median :26.00   Median :28.00  
##  Mean   :20.0   Mean   :25.92   Mean   :26.38  
##  3rd Qu.:29.5   3rd Qu.:28.50   3rd Qu.:30.00  
##  Max.   :39.0   Max.   :35.00   Max.   :39.00

The dataset contains 39 observations of punts. In these observations, the two variable being recorded were distance of air-filled football and the distance of a helium-filled football. We have no missing values in our dataset. The air-filled ball travelled from 15 yards to 35 yards, while the Helium-filled ball travelled from 11 yards to 39 yards. Let’s take a look at a boxplot of the two variables to get an idea of what sort of relationship there is between the two, if any.

boxplot(helium$air, helium$helium)

Our boxplot shows the air-filled ball is more consistent in terms of distance travelled, while we see more variation in the helium-filled ball.

Analysis

Hypothesis: \(H_0: p_1=p_2\)
\(H_A: p_1 \neq p_2\)

Testing our data:

t.test(helium$helium, helium$air)
## 
##  Welch Two Sample t-test
## 
## data:  helium$helium and helium$air
## t = 0.37032, df = 70.666, p-value = 0.7123
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.023751  2.946828
## sample estimates:
## mean of x mean of y 
##  26.38462  25.92308

Our p-value is 0.7123, which means we fail to reject our \(H_0\). Our null hypothesis originally stated that there is no significant difference between distance travelled of air-filled and helium-filled footballs.

Conclusions

Our data suggests that helium-filled footballs and air-filled footballs are not significantly different, so we can say there is a weak correlation between air type of a football and distance travelled.

Does this make sense? Is this a legitimate concusion to deduce? In fact, this makes perfect sense.

Footballs that are filled with air are more dense than footballs filled with helium. Due to helium’s lower density, it would make sense that the air-filled ball travels just as far, if not farther, than the helium-filled ball.

Limitations

Although a very straightforward test, we do find to be quite a few limitations for this experiment. Location would be one, as footballs typically travel farther in higher altitudes. This test was conducted in Ohio, but I’m wondering if performing the same test in Colorado would have different results. Although, weather is also a Limitation here. This test was performed under moderately stable weather conditions, but could inclament weather such as rain or snow have an impact on our results? Whether the test was performed indoors or outdoor is a limitation as well, since punting indoors is generally more favorable than outdoors. Wind resistance begins to play a role outdoors, as a breeze can definitely impact the distance of the kick.

A few other note-worthy limitations would be wether or not the same kicker performed each trial of the data. One punter punting the ball 78 times may or may not cause some fatigue, thus slightly altering our data. This also gives way to more error, as no two kicks will be the same. Also, since only 2 balls were used in the experiment, could the balls experience a decrease in PSI level? Or perphaps a better question is does the PSI level in the footballs make an impact on the results? A flatter football will not generate enough spin to hang in the air for very long.

Lastly, the most important (and most glaring) piece of information that was not omitted in this experiment would be the hang time of the football. While distance travelled is certainly important, the true measure of whether or not the helium-filled ball is going farther depends on the hang time. If a punt has a hang time of 5 seconds, and travels 40 yards, compared to another punt that travels 45 yards but is only in the air for 3.7 seconds, the punt with a longer hang time is in the air for a longer period of time, and thus travels a farther distance.

This document was produced as a final project for MAT 143H - Introduction to Statistics (Honors) at North Shore Community College.
The course was led by Professor Billy Jackson.
Student Name: Enea Jahaj Semester: Fall 2017