Problem — Confidence interval for light bulbs

Text

A sample of $400$ light bulbs has mean lifetime $\bar x=1200$ h with standard deviation $s=300$ h. Construct the $95\%$ confidence interval for the mean lifetime of the population.

Solution

Set-up. The confidence interval for the mean has the form $\bar x \pm z\cdot\frac{s}{\sqrt{n}},$ where $\dfrac{s}{\sqrt{n}}$ is the standard error of the mean and $z\approx 1,96$ is the critical value for the $95\%$ level. Substitute $\bar x = 1200$, $s = 300$, $n = 400$: first compute the standard error $\dfrac{300}{\sqrt{400}} = \dfrac{300}{20}$, multiply it by $1,96$ and add/subtract it to $1200$ to obtain the endpoints of the interval.

Links

Topics: Probabilita
Concepts: Errore standard · Intervallo di confidenza
Skills: Stimare
Exercise type: Problema modellizzazione