Answer to Question #110710 in Statistics and Probability for Vakamuina Sasha Mbatera

Question

Johnson (1966) measured bills of dusky flycatchers and found that bill lengths of the
males had a mean of 8.15 ± 0.021 mm (mean ± SE) and a coefficient of variation of
4.67 %. On the basis of this information, infer how many specimens must have been
used in the sample.

Answer 1

$CV=\frac{\sigma}{\mu}\to\sigma=\mu*CV=8.15*0.0467=0.381.$

$SE=\frac{z_{0.025}\sigma}{\sqrt{n}}\to n=(\frac{z_{0.025}\sigma}{SE})^2= (\frac{1.96*0.381}{0.021})^2=1265.$