Question

In a random sample of 100 forests in the United States, 56 were coniferous or contained conifers. In a random sample of 80 forests in Mexico, 40 were coniferous or contained conifers. Is the proportion of conifers in the United States statistically more than the proportion of conifers in Mexico?

Short answer

Two proportions are being tested.

Step-by-step solution

Given information

• There were 100 random samples of forests in the United States, 56 of which were coniferous or had conifers.
• There were 80 random forest samples in Mexico, 40 of which were coniferous or included conifers.
• To determine whether the United States has a higher proportion of conifers than Mexico.

To identify the most appropriate hypothesis test for the supplied data.

Assuming that the percentage of conifers in Mexico is ${\mathrm{p}}_{\mathrm{M}}$

Assume that the proportion of conifers in the United States is$p_U$

The null and alternative hypotheses are stated as follows:

$$\begin{gathered} {\mathrm{H}}_0:{\mathrm{P}}_{\mathrm{U}}={\mathrm{p}}_M \\ {\mathrm{H}}_{\mathrm{a}}:{\mathrm{PU}}_{\mathrm{U}}>{\mathrm{p}}_{\mathrm{M}} \end{gathered}$$

This demonstrates that there are two proportions in this hypothesis test.