Confidence Interval Coverage Normal

En læringskomponent, der illustrerer dækning af konfidensintervaller for middelværdien af en normalfordeling.

Indstillinger

intro | (node|string): tilsidesætter standard (interaktiv) introtekst. Default: none.
quartileNotation | boolean: styrer, om der skal anvendes alpha/2 som subscript for den kritiske værdi eller blot critical.. Default: true.
sampleStats | boolean: kontrollerer, om man skal kunne skifte mellem at bruge stikprøvens standardafvigelse eller den kendte populationsstandardafvigelse ved beregning af standardfejlen. Default: true.

Eksempler

Live Editor

<LearnConfidenceCoverageNormal />

<LearnConfidenceCoverageNormal />

Resultat

Confidence Interval Coverage for Sample Mean

$X \sim Normal (μ, σ Standard Deviation)$ . Then $\bar{X} \sim Normal (μ, \frac{σ}{\sqrt{n}})$ . Our confidence interval is then $\bar{X} \pm Z_{\frac{α}{2}} \cdot \frac{σ}{\sqrt{n}}$ $\bar{X} \pm t_{\frac{α}{2}} \cdot \frac{S}{\sqrt{n}}$ .For our choice of sample size (n), $μ$ , $σ$ , and confidence level, we will simulate 20 different samples from our normal distribution and calculate the corresponding sample means and confidence intervals.

Change parameters

Sample size (n) :

Mean (mu):

Standard Deviation:

Confidence level:
0.010.99

Confidence Intervals

Of the 20 confidence intervals, 19 capture the true proportion (coverage: 0.95).

Indstillinger​

Eksempler​

Confidence Interval Coverage for Sample Mean

Change parameters

Confidence Intervals

Indstillinger

Eksempler