We've used Student's and Welch's T-Test for A/B tests in the past, but these multi-way tests don't seem to fit the bill. What sort of formula should we be using to compute %confidence for a 3, 4, or 5-way test?

Here's an example test we could run with no obvious control:

Grab every person walking by you on the street and offer them a single fruit. The fruit could be an apple, orange, or pear. If the person is wearing a hat and they would have been offered an orange, they are not allowed to participate in the test. Otherwise, record the fruit type and whether they accepted it.