Sampling distributions & estimators.md (889B)
1 +++ 2 title = 'Sampling distributions & estimators' 3 template = 'page-math.html' 4 +++ 5 6 # Sampling distributions & estimators 7 8 sampling distribution of sample mean: probability distribution of random variable $\bar{X}_{n}$ 9 10 sampling distribution of sample proportion: probability distribution of $\hat{P}_{n}$ 11 12 a sample proportion is $\frac{\text{number of successes}}{\text{total number of observations}}$ 13 14 $\hat{P}_{n} \sim N(p, \frac{p(1-p)}{n})$, with p the number of successes 15 16 ## Confidence intervals 17 18 a way to estimate stuff. e.g. a 95% confidence interval means we are 95% confident that this interval has a true value of μ. 19 20 $CI = \bar{x}_{n} \pm z \frac{s_n}{\sqrt{n}} $ 21 22 Z is the Z-score for the confidence level you want (find this with a table). 23 The margin of error is whatever you add to/subtract from the sample mean. 24 25 To get $s_{n}$, you can use the central limit theorem.