I am working on a project related to the way in which a message to smokers is communicated to reduce their smoking. For my experiment I will give a questionnaire to smokers where, in each question, they will be asked what message motivates them most to quit smoking. Option 1 is a classic message, option 2 is a message designed according to my theoretical framework, and the third option is a neutral option in that both options motivate them equally.

I would like to know, how can I evaluate if the differences, proportionally speaking, are significant? for example, if the total results of the proportions were:

```
classic message ----> 20%

message based on framework --->70%

neutral option message ---> 10%

```

How can I verify that these results are significant? Do I need to do a test for this?

Or can I simply justify it with the margin of error? The margin of error of my sample is 5%. Therefore the distribution at the population level in the worst case would be 65% of the message based on my framework, which would be much higher than the other two options, even if they are in the upper range of the margin of error. Would this analysis be sufficient?

Thanks for your help.