Question

You wish to find a 95% confidence interval for the mean number of times men change channels with a remote control during a commercial. based on a preliminary study, you estimate σ = 15. how many commercials' worth of data do you need to have a margin of error no more than 3?

Answer 1

For margin of error to be a maximum of 3:
3 = z*(SD / sqrt(n)), where z is the z-score, SD is the standard deviation and n is the sample size.
z = 1.96 for a 95% confidence interval, and we are given SD = 15.
3 = 1.96*15/sqrt(n)
sqrt(n) = 9.8
n = 96.04 ~ 96 commercials.