STAT1008 Lecture Notes - Lecture 15: Central Limit Theorem, Standard Deviation, Statistic
Document Summary
Central limit theorem: big population size normal distribution. A normal distribution can be used to approximate the distribution of proportion as long as np >= 10 and n(1-p)>= 10 central theorem limit holds. Proportion result is not known in advance so use p = 0. 5 (gives largest result of. If n > 30 central limit theorem holds. However if original population has normal distribution (skewed, outliers) Usually we don"t know the population standard deviation so use sample statistic standard deviation, s the resulting z score for the sample mean in no longer normally distributed. T-distribution and degrees of freedom: when using sample standard deviation. Higher degrees of freedom t-distribution is closer to normal distribution. T-distribution changes with sample size, unlike normal distribution. Standardizes statistic for a mean: (using sample standard deviation, s, follows a t-distribution with n-1 degrees of freedom)
