The Problem
A school food-services director has come to you with a problem. She thinks that she can increase the consumption of vegetables in the school cafeteria if she works with those vegetables that the children like.
The school serves two distinct populations: one is middle-income families and the other is recent-immigrant families. It will be easier, explains the food-services director, if I can assume that all the children's preferences are about the same.
You use this "children preference equality" as your hypothesis and construct a simple test. A questionnaire lists 22 candidate vegetables. Five students, each 5 years old, from each economic group are chosen at random. Each student is asked to take the vegetable list home to their parents. The instructions accompanying the list are simple. Please cross out any vegetable that you believe your child will not eat.
The lists are returned and the data are extracted.
What can you say about the homogeneity of the children's preferences, according to their parents?
Please Note: The data are made up with no regard for reality.
The Data
The following data are entered with the following conventions:
Item 1 2 3 4 5 6 7 8 9 10
Onion 0 1 1 1 1 1 1 1 0 1
Brussels-Sprouts 0 0 0 1 0 0 1 0 1 0
Zuchini 1 0 0 0 0 0 0 0 0 1
Mushroom 1 0 0 0 1 1 0 1 0 0
Carrots 1 1 1 1 1 1 1 1 1 1
Cucumber 1 1 1 0 1 1 0 0 0 1
Avocado 0 1 0 0 0 0 0 1 0 0
Aspargus 1 1 0 1 1 0 0 0 0 0
Cauliflower 0 1 0 0 0 0 0 0 0 0
Potato 1 1 1 1 1 1 1 1 1 1
Lettuce 1 1 0 1 0 1 1 1 0 0
Peas 1 1 1 1 1 1 1 1 1 1
Spinach 0 1 0 0 0 1 0 1 0 1
Squash 0 1 0 0 0 1 0 0 0 1
Eggplant 0 1 0 0 0 0 0 0 0 0
String-Beans 1 1 1 1 1 1 1 1 1 1
Okra 1 0 0 0 0 0 1 1 0 1
Lima-Beans 1 1 0 1 1 1 0 1 1 0
Green-Pepper 1 1 1 0 1 1 1 1 1 0
Cabbage 0 1 1 1 1 1 0 1 1 1
Corn 1 1 1 1 1 1 1 1 1 1
Tomato 1 1 1 0 0 1 0 0 0 1
Broccoli 0 0 0 1 0 0 0 1 0 1