Normally distributed: population variance known

Let be a random sample of n observation from a normal population with unknown and known variance . Let be the sample mean. Then confidence interval for the population mean with known variances is given by

,

where is the number for which and the random variable Z has a standard normal distribution.

Example:

Given a random sample of 36 observations from a normal population for which is unknown and , the sample mean is found to be .

Construct a 95% confidence interval for .

Solution:

and

From

we obtain that

So, is a 95% confidence interval for .

It means, if sample of 36 observations are drawn repeatedly and independently from the population, then over a very large number of repeated trials, 95% of these intervals will contain the value of the true population mean.

Дата добавления: 2015-08-05