Question

Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 13 specimens of a particular species, 4 resprouted after fire. Estimate with 90% confidence the proportion of all shrubs of this species that will resprout after fire.

Interval:

Answer 1

The sample proportion here is computed as:
p = x/n = 4/13 = 0.3077

From standard normal tables, we have here:
P( -1.645 < Z < 1.645) = 0.9

Therefore the confidence interval here is obtained as:

This is the required 90% confidence interval for the population proportion of all shrubs of this species that will resprout after fire.