# Pizza Statistics

Ted Lawrence and Paolo Fu

Professor Bruff

Math 216

Application Project Part One

March 26, 2012

Pizza Deserts

Does income level affect average pizza price in a given area? Also, does income level affect the concentration of pizza restaurants in an area?

For our project, we are interested in finding the relationship between the average price of a large cheese pizza pie and the average annual income for given areas in Davidson County. We will also investigate the influence of average annual income on the number of pizza places in that area.   The areas we will use in our analysis will be the same as those used in the 2000 national census also referred to as census tracts. The average annual income information for these census tracts will come from the 2000 census and is accessible through the map network drive on the Vanderbilt campus network. According to Yellowbook there are 187 pizza restaurants within Davidson County. We will conduct a survey of the pizza prices for all or most of these locations by phone. This data will be input into the program ArcGIS in order to visualize it on a map of Davidson County. Two linear regression models will be created to analyze the relationship between number of pizza places and income level, and the relationship between the average pizza price and income level for each with each census tract as a data point.

ArcGIS is a geographic information system (GIS), which is a “system designed to capture, store, manipulate, analyze, manage, and present all types of geographical data” (Wikipedia 2011).  This program is available to students in the Featheringill computer lab and is taught in CE 161, civil and environmental information systems II which Ted is currently enrolled in. If extra assistance for this program is needed, we will contact Jacob Thornton, GIS coordinator for Vanderbilt University.

Where are the pizza deserts?

With ArcGIS we will be able to create a heat map of Davidson County showing average annual income for the census tracts. We can then overlay the pizza restaurant locations, based on their addresses, onto this heat map.  Using this map, we can determine the average pizza price within a given census tract by averaging the pizza prices of the restaurants located within that tract. A second heat map will be created to show average price of pizza within the census tracts. Census tracts that aren’t within close proximity to a pizza restaurant will be referred to as “pizza deserts” due to their lack of access to pizza.

Is the average price of pizza different in Williamson County?

In addition to the above research, a random sample of 10 pizza restaurants in Williamson County will be taken. With this data we will find the mean and standard deviation of the sample pizza price. We can then perform a hypothesis test in order to potentially answer the above question. Our null hypothesis H0 will be that average pizza price in Davidson County is equal to the average pizza price in Williamson County. Our alternative hypothesis HA will be that they are not equal to one another. We will use a 5% significance level for this test.

Through this investigation we hope to give our fellow college students the chance to avoid these dreaded pizza deserts, the most inhospitable of environments.

References