The question is: how to calculate the statistical significance of difference between percentages in the case described below?
Suppose we have a poll question with $n$ answer options $A_1, …, A_n$, where a respondent can choose up to $k$ options simultaneously ($1 \leq k \leq n$). The option $A_x$ scored $x$% of votes, and the option $A_y$ scored $y$%. (In general, any respondent might choose both $A_x$ and $A_y$.)
How to calculate whether the difference between $x$ and $y$ is significant at a given significance level (say, .95)? I asked a question similar to this one formerly, but only the case $k = 1$ was considered then. Now I look for a test for more general case.
UPD. Here is a live example from my current research:
247 respondents have answered the question about their preferred kind of investments. 170 of them chose hospitality property, and 124 chose retail property. There were 3 more options in the question (5 total), and each respondent was able to choose up to 2 options. So is the difference between 124 and 170 statistically significant enough to say that hospitality property is more popular asset than retail? How to find out?