Question

STATISTICS. CONFIDENCE INTERVALS.

Let $\left ( X_{1},X_{2},...,X_{n} \right )$ be a simple randon sample of a population with distribution  $N\left ( \theta ,\sigma ^{2}= 100 \right )$.

Construct a credible region with probability 0.95 for the mean $\theta$ , if it is assumed that initial distribution for $\theta$ is $N\left ( \mu _{0}= 100,\sigma _{0}^{2}= 225 \right )$.

Thank you for your explanations.

Answer 1

here, mean = 100
and std. dev. = sqrt(225) = 15

z-value for 95% CI is 1.96 (here z-value indicates the area in the left/right tail is 0.025)

CI = (mean - z*sigma, mean + z*sigma)
= (100 - 1.96*15 , 100 + 1.96*15)
= (70.6 , 129.4)