Curtis Northcutt

Peter York

Hayden Kelly

MATH 216 - Statistics, Dr. Derek Bruff

Statistics Project Proposal

March 26, 2012

**Big Bully on Campus: Is Vanderbilt Stealing Your Lunch Money?**

Math 216 Statistics Project Proposal

**Does the average student lose money on a given meal purchased using meal plan at Rand? **This project focuses on the average cost paid for a single meal plan vs. the average cost of a single meal at RAND. While we note that it is commonly held that the price of a given meal does not accurately reflect the market value of the food purchased (i.e. on-campus food is generally believed to be overpriced), the analysis of whether or not this is actually the case is beyond the scope of the project. Rather, our goal is to advise students who have decided to eat on campus whether to purchase meal plan next semester or use Commodore Cash for food purchases based on the results of our experiment. Thus, a successful statistical analysis of the population of Vanderbilt students who eat at RAND will allow such students to save money next semester on their meal expenses.

We will watch the registers in Rand on Monday and Tuesday, gathering samples consisting of three pieces of data: (1) the price of the meal, (2) the number of remaining meals, and (3) the gender of the person purchasing the meal. Because we do not know the distribution of meal price, will gather 100-200 samples to assume normality. If a student does not use meal plan, we will not gather any data for that student as they are not in the population we are considering. We will gather samples at breakfast and lunch only, because if we gathered data on the only night that Rand serves dinner, Tuesday, our data would likely be unreasonably linearized due to the homogeneity of prices on Tortellini Tuesday. By gathering data on Monday and Tuesday, we will be able to ascertain the percentage of students with each type of meal plan (8, 14, 19, or 21 meal plan) from the number of remaining meals data. Since all Vanderbilt meal plans reset at 12:00 a.m. on Monday, it will not be possible for students to have used enough meals by Monday afternoon in order for their “meals left” to drop below their meal plan category. This project may be extended to analyze other variables by also answering the questions: “Do males or females lose more money on meal plan?” and “Would our results be different if we sampled from Branscomb Munchie Mart instead?”

We will calculate the average cost per meal for all students based on the price for each plan, provided by Vanderbilt Dining^{[1]}. We will then construct a probability distribution function, where x = the average cost per meal for a given meal plan type and P(x) = the percentage of students who have that meal plan. The expected value of this PDF is the average cost per meal for all Vanderbilt students on meal plan.

We will then perform a hypothesis test to determine whether the average cost and average price of a given meal are in line with each other. We will let H_{0 }: μ = E(x), where µ is the average price per meal and E(x) is the average cost per meal, as calculated above. This choice for our null hypothesis stems from Vanderbilt’s assertion that the meal plan average cost approximates your expenditures. We will let H_{A}: μ < E(x), the average price per meal is less than the average cost per meal. By modeling the normal distribution, we will conduct a hypothesis test to determine if there is statistically significant evidence to reject H_{0} in favor of H_{A} with α = 0.05.

If we fail to reject the null hypothesis, we will advise students who eat on campus to stick with meal plan; however, if we reject the null hypothesis, we will advise students to purchase their meals with Commodore Cash and save the difference between the cost of meal plan and the price of dining hall food. While it would be more exciting to be able to reject the null hypothesis if we fail to reject the null hypothesis, it would be gratifying to learn that the university is not taking advantage of students.

**References**

[1] Vanderbilt University. VU Meal Plans. Retrieved from http://www.vanderbilt.edu/dining/vumealplans.php