Question

(1 point) 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 16 specimens of a particular species, 7 resprout after fire. Estimate with 99% confidence the proportion of all shrubs of this species that will resprout after fire.

Answer 1

Answer:

The answer is "$0.45 \pm 0.18204$"

Step-by-step explanation:

For the +4 sample proportion$= \frac{(7+2)}{(16+4)} = \frac{9}{20} = 0.45$

Sample percentage measurements estimated stdev

$= \sqrt{\frac{[(0.45)(1-0.45)]}{[(16+4)]}}\\\\ = \sqrt{\frac{[(0.45)(0.55)]}{[(20)]}}\\\\ = \sqrt{\frac{0.2475}{20}}\\\\= \sqrt{0.012375}\\\\=0.111$

Calculating the critical z for a=0.1, two-tailed = 1.64

Calculating the confidence interval:

$= 0.45 \pm 0.111 \times 1.64 \\\\= 0.45 \pm 0.18204$