Статистика! a sample of 1300 people is to be used to estimate the proportion of left-handed people. suppose the true proportion of left-handed people in the population is 12% (which is unknown to the organizers of the observational study). a) what is the probability that as a result of the survey, the estimate will differ by more than 2% from the true value 12%? use the normal approximation to solve this problem. b )what should be the minimal sample size to guarantee that the obtained estimate doesn't differ by more than 2% from the true value 12% with probability at least 99%?
Дисперсия D= npq= 1300*0.12*0.88=137.28
сигма = √D= 11.72
два процента от тысячи трехсот это двадцать шесть или 26/11.72= 2.22 сигмы. Смотрим по таблице нормального распределения - это вероятность 0.9736
По той же таблице смотрим сколько сигм вероятность 0.99
- это 2.58 сигмы.
0.02*N= 2.58√(Npq)
N=1758 - округляем в большую сторону.