Solution Assignment 01 of the basics of statistics

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The 95% confidence interval of the mean $\mu$ of a normally distributed population is $[106.16; 109.84]$ . The population standard deviation $\sigma$ is given and equals $20.2$ .

What has been the sample size? Explain your answer.

Solution.
The confidence interval is $\displaystyle{\overline{x}\pm{z_{\alpha/2}}\frac{\sigma}{\sqrt{n}}}$ . From the given interval we may conclude that $\overline{x}=108$ , right in the middle of the interval. So, $\displaystyle{z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ . Furthermore, we know that $z_{\alpha/2}=1.96$ and $\sigma=20.2$ . We find $\displaystyle{n=(\frac{z_{\alpha/2}\sigma}{1.84})^2=463}$ .

Return to Assignments The basics of Statistics

Solution Assignment 01 of the basics of statistics

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