Statistical test for survey question with 3 response option 'Yes' 'No' 'Not sure' I am looking for solution for a problem related to social science survey. The problem is.... Suppose my hypothesis is “Majority of customers prefer my new product” – which I want to establish through statistical test. So I have set the question in questionnaire that [“Do you prefer my new product?” with 3 response options ‘Yes’, ‘No’, ‘Not sure’] and completed a survey from 100 respondents. From which I received that 80% respondents replied for ‘Yes’, 15% for ‘No’ and 5% for ‘Not sure’. Now what statistical test should I do to establish the above result so that I can conclude that “Majority prefer my new product”, is it Binomial Test, or One-sample T Test, or Z Test, or something else? Please help in details.
 A: You map the responses to your definition of 'prefer':
    Response:             Prefers new product?
     Yes                   yes
     Don't know            no
     No                    no

Keep in mind that a majority is >50%. Obviously you're not interested in whether  a majority of your sample prefers it (you don't need a statistical test for that). You want to see if your sample result is more than could be explained by random variation about a population quantity that wasn't a majority.
The next thing to worry about is whether you're doing a one-sided or two-sided test. From what you say in your question I assume you want one-sided - that is, to test the null that no more than 50% of the population prefer the new product against the alternative that a majority prefer it. It may be that instead you want to pick up a majority in either direction, which would be a two-sided alternative.
So for the one-sided test you have 
$H_0: \text{no more than 50% prefer the new product}\qquad$   versus
$H_1: \text{a majority prefer the new product}\qquad$ 
And you compare your sample proportion (of 80 out of 100) with the highest population proportion under the null.
You'd use a binomial test for this, though with $n=100$, you'd be able to use the normal (z-test) approximation.
