Introduction Everyone requires food to survive. For those who have had psychology, this was mentioned as being at the very base (biological/psychological needs) of Maslow's Hierarchy of Needs. For those of you who haven't had psychology, try going for any length of time without food and you will see how important it is. Although people are eating out more, the average American still ate 873 meals at home in 2014. Some people may eat out every meal but many of us don’t have the budget to support that and must buy our own food at the grocery store. A naturally arising question is "Is one grocery store cheaper than another?" That's the question we're going to set out to answer in this project. Hopefully we'll have some fun and learn something about statistics along the way. This is a project involving many of the aspects of Statistics. It will involve planning an experiment, collecting data, describing the data, analyzing the data, and making inferences from the data. Phase 1 - Grocery List (10 pts) Your first assignment is to come up with a typical grocery list for your family. The grocery list must contain at least 20 items and at least three items from each of the major categories, although you are encouraged to make it as realistic and lengthy as possible. If you don't do the grocery shopping in your family, then talk to the person who does for an idea of what to put on the list. These will be compiled into a master list that will be used to compare grocery prices. Sample Grocery List Grp Item 1 Chicken 1 Crackers 1 Hamb. Helper 1 Ketchup 1 Macaroni 1 Pepsi 1 Soup 1 Spaghetti 2 Dish Detergent 2 3 3 3 3 4 4 6 7 9 10 Toilet Paper Batteries Light Bulbs Toothpaste Tylenol Hamburger Pork Chops Bananas Bread Milk Pizza Assign each item on your grocery list into one of the following categories: GROCERY (39.72%)* 1. Dry Grocery (Food) 2. Dry Grocery (Non Food) GM/HBC (General Merchandise / Health & Beauty Care) (9.66%)* 3. GM/HBC (includes prescriptions) PERISHABLES (49.67%)* 4. Meat/Fish/Poultry 5. Service Deli 6. Produce 7. Baked Goods 8. In-Store Bakery 9. Dairy 10. Frozen Foods *The percent values following the major categories represent the percent of 2014 sales that category accounted for. You may include name brands if you shop for name brands. Phase 2 - Data Collection (20 pts) Once the master list is compiled, each student should go to 3 different grocery stores and find the prices for the items on the list. One of the stores should be your default store (ie – the store that you would visit most). Follow these guidelines for collecting data. (If you can’t physically go to the grocery store, you can research the price for a store online and use that information if it is available. However, actually visiting the grocery store may be easier)     If a specific name brand is not listed, choose the cheapest brand. If there are two sizes available, choose the larger size. If there are more than two sizes available, choose the medium (second smallest) size. Some stores have membership cards with special reduced prices. Use the reduced prices where available.  Record the number of brands and total number of offerings for each item. We will use this to compare selection as well as price. For example, consider ketchup. Let's say a store has Hunt's (40 oz and 24 oz), Heinz (24 oz, 32 oz, and 48 oz), and a generic (24 oz and 32 oz). We would enumerate three brands and seven offerings. All 3 stores will be visited during the same week. After the data has been collected, it should be listed in an Geogebra File. You will enter the following columns in the spreadsheet function of Geogebra and will create 3 separate Geogebra files (one for each store). Phase 3 - Descriptive Statistics (20 pts) Complete these questions for each of the 3 stores you visited. 1. Generate a side-by-side boxplot for the prices of each of the three main categories of groceries. Comment on any similarities or differences. 2. Generate a summary table of the price with the mean, sample size, standard deviation, minimum, median, maximum, and total (sum) for each of the major categories of food. Comment on any similarities or differences. 3. Generate a histogram with a normal curve displayed for all of the price data from your store. Does the data appear normally distributed? You will probably want to save your output as you go along so that you don't accidentally lose anything if the computer crashes. Phase 4a - Inferential Statistics, part 1 (15 pts) 1. Does the mean price of your default store differ significantly from the mean of the other two stores? Justify your answer. 2. Does your default store have a larger brand selection than the other two stores? Go through and compare the brands at your default store against each of the other stores. There will be one less comparison than the number of stores, so if there are four stores, you will make three comparisons. Justify your answer. 3. Are the prices for each of the three grocery categories normally distributed? Justify your answer. Phase 4b - Inferential Statistics, part 2 (15 pts) 4. Is there any relation between the store and the major food classification with respect to the number of item offerings? Justify your answer. 5. Is there a significant difference in the mean prices of the stores? If there are significant differences in the mean prices, which stores are different? Which is the cheapest store? Which is the most expensive store? Justify your answer. 6. Perform a two-way analysis of variance to answer the following questions. Use the price as the dependent variable and the store and major food categories as fixed factors (independent variable). Justify your answers. a. Is there a difference in the prices between the stores? b. Is there a difference in the prices between the major grocery categories? c. Is there any interaction between the store and major grocery categories? Phase 5 - Project Evaluations (30 pts) Project Evaluation (10 points) In a reflection type essay, comment on the entire project. As a minimum, address questions like 1. 2. 3. 4. 5. Was there any data that was collected that wasn't needed? Was there data that wasn't collected, but it would have been nice to know? What changes would you make the next time this project is done? Was the project relevant / interesting? Are there topics that you would like to see investigated? 
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