Example 6.5

EXAMPLE 6.5 How Can we Reduce the Standard Deviation of the Sample Mean?

In the setting of Example 6.4, if we want to reduce the standard deviation of $\bar{x}$ by a factor of 4, we must take a sample 16 times as large, $n = 16 \times 100$ , or 1600. Then

$σ_{\bar{x}} = \frac{25.83}{\sqrt{1600}} = 0.65 minute$

For samples of size 1600, about 95% of the sample means will be within twice 0.65, or 1.3 minutes, of the population mean $μ$ .