b:head_first_statistics:estimating_populations_and_samples
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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 | ||
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===== 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: | ||
$$\overline{X} \sim N(np, \; pq) $$ | $$\overline{X} \sim N(np, \; pq) $$ | ||
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</ | </ | ||
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.1668523487.txt.gz · Last modified: 2022/11/15 23:44 by hkimscil