Question

a researcher wanted to study the tendency of our choices to be influenced by our environment, so she conducted an experiment. the researcher recruited 90 volunteers. she randomly assigned 30 to sit in a room with red walls, 30 to sit in a room with yellow walls, and 30 to sit in a room with orange walls. after sitting in the room doing mundane activities, she offered them all a snack of strawberries, bananas, or oranges. for each individual, she recorded which room the participant was in and which snack they chose. the data are displayed in the table. the researcher would like to know if these data provide convincing evidence that the distribution of snack choice differs for the various room colors in the population of all volunteers like these. what is the appropriate inference procedure? chi - square test for goodness of fit because the data come from one random sample chi - square test for homogeneity because the data come from independent treatment groups chi - square test for association/independence because the data come from one random sample

Explanation:

Step1: Understand the tests

• Chi - square test for goodness of fit: Used when we have one categorical variable and we want to test if the distribution of that variable follows a hypothesized distribution. Here, we have two categorical variables (room color and snack type).
• Chi - square test for homogeneity: Used when we have multiple independent groups (here, the groups are the different room colors) and we want to test if the distribution of a categorical variable (snack type) is the same across these groups.
• Chi - square test for association/independence: Used when we have one sample and two categorical variables to test if there is an association between them. But in this case, the groups (room colors) are independent treatment groups (created by random assignment), not just one sample split into subgroups based on two variables.

Step2: Analyze the data structure

The researcher has three independent groups (room colors: red, yellow, orange) and is looking at the distribution of snack type (another categorical variable) across these groups. This is the setup for a test of homogeneity.

Answer:

chi - square test for homogeneity because the data come from independent treatment groups