STOR 155 Lecture Notes - Lecture 19: Standard Deviation, Triangular Distribution

• School: UNC
• Department: Statistics And Operations Research
• Course: STOR 155
• Professor: All

Document Summary

Stor 155: introduction to statistics lecture 19: analysis of the trade-off. Population: has variance v{x, has standard deviation s. d. N observed x values: sample mean calculated from n observed x values, sample mean is a statistical estimate of e{x} The trade-off: having a large sample size makes sample mean closer to e{x, having a large sample size costs a lot of money, cost of taking large sample, manpower, materials, time, destruction of subject. The fundamental probability equation: p { e{x} d < sample mean < e{x} + d } = p. In other words, you want sample mean to be within the range of d to +d p probability of the time. {sample mean} < sample mean e{x} / s. d. {sample mean} : { -c < z < +c, plug it back in, p {-c < z < +c, c = (1/2) (1+p, c = d / s. d. {x} / sqrt(n: n = c2 v{x} / d2.