kb:confidence_interval

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kb:confidence_interval [2022-02-12 21:23] – created jaeyoungkb:confidence_interval [2024-04-30 04:03] (current) – external edit 127.0.0.1
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 $$ \mathbb{P}(\hat{\Theta} - 1.96 \hat{\mathrm{se}} \leq \theta \leq \hat{\Theta} + 1.96 \hat{\mathrm{se}}) \approx 0.95 $$ $$ \mathbb{P}(\hat{\Theta} - 1.96 \hat{\mathrm{se}} \leq \theta \leq \hat{\Theta} + 1.96 \hat{\mathrm{se}}) \approx 0.95 $$
  
-So the confidence interval is:+So the $95\%$ confidence interval is:
  
 $$ [ \hat{\Theta} - 1.96 \hat{\mathrm{se}}, \hat{\Theta} + 1.96 \hat{\mathrm{se}} ] $$ $$ [ \hat{\Theta} - 1.96 \hat{\mathrm{se}}, \hat{\Theta} + 1.96 \hat{\mathrm{se}} ] $$
 +
 +The approximation $\mathrm{se} \approx \hat{\mathrm{se}}$ may cause significant deviation.
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  • Last modified: 2024-04-30 04:03
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