b:head_first_statistics:estimating_populations_and_samples
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| b:head_first_statistics:estimating_populations_and_samples [2022/11/15 23:44] – [Sampling distribution of sample mean] hkimscil | b:head_first_statistics:estimating_populations_and_samples [2022/11/17 12:47] (current) – [Exercise] hkimscil | ||
|---|---|---|---|
| Line 326: | Line 326: | ||
| ===== Using CLT for the binomial distribution ===== | ===== Using CLT for the binomial distribution ===== | ||
| - | $X \sim B(n, p)$, n이 30이 넘는 조건에서, $\mu = np$, $\sigma^2 = npq$ 이므로 | + | $X \sim B(n, p)$ 에서 $\mu = np$, $\sigma^2 = npq$ 이고, |
| + | n이 30이 넘는 조건에서 이항분포가 정상분포를 이룬다고 하므로 | ||
| + | $\overline{X} \sim N(\mu, \frac{\sigma^2}{n})$에 대입해 보면: | ||
| $$\overline{X} \sim N(np, \; pq) $$ | $$\overline{X} \sim N(np, \; pq) $$ | ||
| Line 364: | Line 366: | ||
| </ | </ | ||
| discrepancy? | discrepancy? | ||
| + | < | ||
| + | > a <- sqrt(1/30) | ||
| + | > b <- 8.5-10 | ||
| + | > b/a | ||
| + | [1] -8.215838 | ||
| + | > pnorm(b/a) | ||
| + | [1] 1.053435e-16 | ||
| + | |||
| + | </ | ||
b/head_first_statistics/estimating_populations_and_samples.txt · Last modified: 2022/11/17 12:47 by hkimscil