Given that there are 1, 485 people you need to take for a survey for their drink preferences. Determine the sample if the error tolerance is 5%

Question

how to calculate this help

Answer 1

Have to make a LOT of assumptions.

I'll assume that the samples will be taken by simple random survey with a dichotomous choice.

Null hypothesis is that there is NO Preference between two drink preference choices.

Alternate hypothesis is that either one or the other drink choice is preferred.

Alpha is 2% (Confidence = 98%).

Error tolerance = margin of error (moe)

"determine the sample" is a typo error and should be "determine the minimum sample size"

The drink choices don't matter but for those who like to have that we will assume one choice is wine/beer and the other choice is "hard liquor"

Using cochran's formula. n₀ = Z²pq/e²

(e = error tolerance [.05], Z = critical z for two sided 98% CI or 2.327)

p = .5 (non-assuming prior). q = 1-p = .5

minimum sample size = 542

note: if we were looking for a moe of 5% and an alpha of 5% the answer would be only 385