A biologist wants to estimate the difference between the mean body lengths of green and brown stinkbugs. A random sample of 20 green stinkbugs has a mean body length of 16.22 millimeters (mm) and a standard deviation of 1.34 mm. A random sample of 20 brown stinkbugs has a mean body length of 13.41 mm and a standard deviation of 0.73 mm. What is the standard error of the difference (green \(-\) brown) between the sample means?

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Use the formula for the standard error for the difference of two populations. This is given in the formula page, so no need to memorize.

$$ s_{\bar{X_1}-\bar{X_2}} = \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} $$ $$ = \sqrt{\frac{(1.34)^2}{20}+\frac{(0.73)^2}{20}} $$

Adding the fractions results in the correct answer.