X has recently opened a restaurant. She is interested in listing her restaurant with various online vendors, but anticipates that the listing will receive a better rating in terms of perceived healthiness based on a halo effect. That is, she feels that her rating will be biased simply because it will be associated with other restaurants that share the same categorisation as her.
Some people have described her restaurant as a café. Some have referred to her as a pizzeria, whilst others suggest its best to describe her restaurant as "Italian".
She worries that if people see her categorised as a pizzeria they will infer it as being less healthy relative to having a listing categorising her as "Italian" or as "Coffee/Café".
In turn, Christine is now interested in examining the evaluation of restaurants with respect to their perceived levels of healthiness and these three cuisine types.
- Can you formally test whether a perceived level of healthiness is independent of whether the cuisine is classified as 'Pizza', 'Italian' or 'Coffee/Café'? What is the relevant information needed to formally test for independence?