Confidence interval with known variance

Problem

A sample of size $n=100$ has mean $\overline{x}=10$ . The population standard deviation is known to be $\sigma=2$ . Compute the two-sided $95\%$ $z$ confidence interval for the population mean using $z=1.96$ , and interpret it correctly.

Reveal answer or reference solution

The standard error is $2/\sqrt{100}=0.2$ , and the interval is

10 \pm 1.96(0.2) = [9.608,10.392].

Under repeated sampling, $95\%$ of intervals constructed this way contain the fixed population mean.

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Statistics Practice