Question

Birds in the trees Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, $54\%$ of the trees are Douglas firs, $40\%$ are ponderosa pines, and $6\%$ are other types of trees. At a randomly selected time during the day, the researchers observed $156$ red-breasted nuthatches: $70$ were seen in Douglas firs, $79$ in ponderosa pines, and $7$ in other types of trees.

a. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they’re searching for seeds and insects?

b. Relative to the proportion of each tree type in the forest, which type of trees do the nuthatches seem to prefer the most? The least?

Short answer

Part (a) There is enough data to back up the assumption that nuthatches prefer certain tree species.

Part (b) Because its proportion is higher, it is the most chosen nuthatch. Other sorts of trees are the least desired because their proportion is so little.

Step-by-step solution

 Part (a) Step 1: Given information

Part (a) Step 2: Explanation

The null and alternative hypotheses:

$$\begin{gathered} H_0:p_0=0.54,p_2=0.4,p_3=0.06 \\ {H}_a:Atleastoneofthe{p}_i’sisincorrect. \end{gathered}$$

Using excel,

Decision: $P-value<0.05,reject{H}_0$

There is enough data to back up the assumption that nuthatches prefer certain tree species.

Part (b) Step 1: Explanation

Douglas firs appear to be the most favored nuthatches in terms of relative proportion, as their proportion is higher. Other sorts of trees are the least desired because their proportion is so little.