Is there a way to test the "accuracy of a binomial survey"?
I've been away from mathematics for a while and forgotten almost everything. It doesn't come from a text book; I was given an assignment in my training for a job and wondered if I can use my mathematical knowledge. All I have to do is actually interpret the data and say "more than 50 percent of the people surveyed thinks "yes" to the question" but I'm taking a step further and trying to say how "accurate" is the result? Basically, here's what I am given
There's a supermarket that is experiencing a fall in revenues. A survey was conducted and it asked whether "the customer thinks the workers are unfriendly/unhelpful." out of a 100 randomly chosen customers on the same day (100 different customers) 51% answered "yes."
However, the total number of customers that visited the supermarket is expected to be around 485. The total that visited the supermarket that month is 19700. How confident are we to say that more than 50% are not happy with the workers among all of those who visited the store a. that day b. that month?
I vaguely recalled Chi-squared ad z-test but I wasn't so sure; I tried the z-test with
where p=0.51,π=0.5,n=100. Thing is, I get z=0.2 and the z table seems to tell me this is a very inaccurate result. In any case, my data and the question I ultimately want to answer is as above. Along the process of doing so, if no one would want to actually show me how to do this, can you please answer
What's the most apt test to answer a question like this? And why?
I think, as people start writing some answers, my senses will come back, some words and terms ringing a bell, reminding me of certain formulas, rules etc.