Question

You have just performed a survey interviewing 358 randomly selected people. You found that 94 of them are interested in possibly purchasing a new cable TV service. How much uncertainty is there in this number “94” as compared to the average number you would expect to find in such a survey? (You may assume that exactly 25% of all people you might have interviewed would have been interested.)

Answer 1

Solution :

out of 358 randomly selected people we found that 94 of them are interested in possibly purchasing a new cable TV service.

N = 358

X = 94

sample proportion = p = X/N = 94/358

p = 0.2626

Uncertainity in X = sample standard error under binomial distribution

Calculating Uncertainity in X = 94:

= √(N*p*(1-p)) = √(358*0.2626*(1-0.2626)) = 8.326

Calculating uncertainity in the average number we would expect to find in such a survey : (here p = 0.25)

= √(358*0.25*(1-0.25)) = 8.193

The uncertainity in observed number (=94) is 8.326 which is slightly larger than as compared to the uncertainity in the expected number (uncertainity = 8.193)