Question

Ten samples of coal from a northern appalachian source had an average mercury content of 0.242 ppm with a standard deviation of 0.037 ppm. find a 95% confidence for the mean mercury content of coal from this source. round the answers to four decimal places. the 95% confidence for the mean mercury content of coal from this source is

Answer 1

The confidence interval is from 0.2191 to 0.2649, given by

$0.242\pm0.0229$.

The z-score we need is found by first subtracting the confidence level from 1:
1 - 0.95 = 0.05

Divide that by 2:
0.05/2 = 0.025

Subtract that from 1:
1 - 0.025 = 0.975

Look this up in the middle of a z-table (http://www.z-table.com) and we see that the z-score is 1.96.

Now our confidence interval is given by
$\overline{x} \pm z\times \frac{\sigma}{\sqrt{n}} \\ \\0.242\pm 1.96 \times (\frac{0.037}{\sqrt{10}}) \\ \\0.242 \pm .0229 \\ \\0.242-0.0229=0.2191 \\ \\0.242+0.0229 = 0.2649$