dixon stats project

8/13/2019 Dixon Stats Project

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Introduction

Geaux Tigers is a common phrase uttered on a Louisiana Saturday Night. Students,

Alumni, and Tiger Fans fill Death Valley to cheer the LSU Fighting Tigers to victory. The LSU

Athletic Department generously offers two student ticket options: general admission or reserved

group seating. The general admission ticket costs $12 per a game and the seats are on a first

come first serve basis. The student section games open three hours before a game and students

must get in line early to get the prime seats for big games. The other option that the LSU

Athletic Department offers is the reserved group seating. Reserved group seating is for

organizations and their members to have the ability to sit together in a guaranteed seat that is

consistent throughout the season. These tickets cost $18 per game; however, the student has a

reserved seat and does not have to worry about getting in line early to get a better seat.

I am interested in seeing if there is a difference between when you leave based on your

seat. I have hypothesized that people who have general admission student tickets typically leave

the game early. I believe this because many of these general admission students have been in the

stadium longer than students who have reserved group seating, since they had to arrive early to

get a desired seat.

Data Collection

Using a Qualtrics survey, I obtained 97 survey respondents for my survey data. Forty of

the respondents were students who had reserved group seating tickets, 40 students had general

admission student tickets, and 17 of the respondents did not have student tickets. For the

purpose of my research, I discarded the respondents who did not have student tickets. The game

day habits of each student were classified into two groups: students who typically leave the game

early or students who do not typically leave the game early.

Table 1. Number of People


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# Population Leave game early Do not leave game early Total

1 General admission student seating 30 10 40

2 Reserved group student seating 20 20 40

Total 50 30 80

Descriptive Statistics

1. Graphical Representation

The following figures display my data on the entire population, and the proportion of the

general admission student tickets and the reserved group seating student tickets who typically

leave the game early or dont typically leave the game early.

Figure 1. Histogram for students who typically leave the game early versus not leaving the

game early

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Figure 2. Proportion of general admission students leaving the game early vs. not leaving the

game early

Figure 3. Proportion of reserved group student tickets leaving the game early vs. not leaving

the game early

2. Numerical Measure

Table 2. Probability Table

Population Yes No Total

1 General admission student seats 37.50% 12.50% 50.00%

2 Reserved group seating 25.00% 25.00% 50.00%

Total 62.50% 37.50% 100.00%

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Table 2 shows the probability of the relative frequency of each occasion. The probability results

are constrained by the number of respondents who choose to answer the survey. However, with

a sample size n=80, I calculated the sample proportion of people leaving the game early as

follows:

! !!

!

!

!"

!"! !"!!"#

Statistical Inferences

1. Confidence Interval Estimations

With != proportion of students leaving the game early, which is an unknown, fixed value, I

set my confidence level at 95%, as shown by the following normal distribution.

The margin of error can be solved using the formula below. I have determined the margin of

error for this study in 10.609%.

Margin of Error: !!!!" !!!!!!!!

!

! !10.609%

J

-1.96 +1.96

95%


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The formula below solves for the 95% confidence interval of !. It can be concluded with 95%

confidence that 51.891%-73.10% of the population typically choose to leave the game early

rather than stay.

! ! !!!" !!!!!!

!

! !!"#$! !!!" !!"#!!!"#!!"

!51.891% ~73.10%

2. Hypothesis Testing

the proportion of general admission students who typically leave the game is greater than 50% of

the total students who leave the game early.

Null Hypothesis: Ho:!! !

!!

Alternate Hypothesis: H1: !!!!!

Test Statistic :

! !!!!!

!!!!!!

!

= 2.315

One sided p-value= p[Z>.9898]=.0102

Conclude: H1 because the proportion of general admission students who typically leave the

game is greater than 50% of the total students who leave the game early.

3. Hypothesis Testing of Two Population Case

We still need to resolve whether or not there is a difference in game day habits between the

population of students who have general admission tickets or reserved group seating tickets.

Null Hypothesis: !!!! ! !!Alternate Hypothesis: !!!! ! !!

Decision Rule:

If (Z) ! !!!", then conclude !!. Otherwise, conclude !!.

Test Statistic:


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!!!

!!!!! !!

!!!!!!!!

!!

!!!!!!!!!

!!

, with d=.5!!!"!!!!!!!

!!"!!!"!

!"!!!!!!!

!"

! !!!!"

Two sided p value=.0168

Conclude H1 there is a difference in how many people typically leave the early between general

admission student tickets and reserved group seating

Conclusion:

According to my data, my hypothesis has been supported and there is a significant

difference between leaving the game early and whether you have general admission student

tickets or reserved group seating. There is a correlation between reserved group seating and

general admission tickets and their decision on whether or not to leave the game early. Students

leaving games early is starting to become an epidemic among college football. Students who

have reserved group seating tickets do not typically leave the game early as often as general

admission tickets. This can be contributed to a number of factors including heat and exhaustion.

Maybe if LSU offered a reserved seating option to more students, than this problem can be

alleviated and more students would cheer the Tigers on to victory.


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