T the Foraging Capability of Downy Woodpeckers Can Be Compromised $1.5 \mathrm {~g}$

Essay

T The foraging capability of Downy Woodpeckers can be compromised if part of their habitat disappears due to significant human encroachment. These creatures eat insects in trees, and if they cannot find enough food due to a decreasing forest area their body mass may decrease. A previous study of Downy Woodpeckers indicates that for male Downy Woodpeckers the population standard deviation of body mass is approximately $1.5 \mathrm {~g}$ . Suppose that an estimate $\mu$ , the current average mass of male Downy Woodpeckers in a local forest preserve, is desired. If the previous study value is taken as a reasonable first estimate of the population standard deviation, what is the minimum sample size that is necessary to estimate $\mu$ to within $0.2$ grams with $95 \%$ confidence?