Let's say we know this:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right)

[/tex]

How do we get from this information to this expression of confidence interval for [itex]\theta[/itex]?

[tex]

\left( \widehat{\theta} \pm u_{1-\frac{\alpha}{2}}\frac{1}{\sqrt{nF\left(\widehat{\theta}\right)}}\right)

[/tex]

Where [itex]u_{1-\frac{\alpha}{2}}[/itex] is appropriate quantil of standard normal distribution.

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Confidence interval

**Physics Forums | Science Articles, Homework Help, Discussion**