Confidence interval with known variance

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Problem

A sample of size $100$ has mean $10$ . The population standard deviation is known to be $2$ . Construct the usual two-sided $95\%$ $z$ -confidence interval for the population mean.

Reveal answer or reference solution

The standard error is $2/\sqrt{100}=0.2$ . Using $z_{0.975}=1.96$ gives

10\pm1.96(0.2)=10\pm0.392,

so the interval is $[9.608,10.392]$ .

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Confidence interval with known variance

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