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

The answer is "
`0.45 \pm 0.18204`"

Explanation:

For the +4 sample proportion
`= ((7+2))/((16+4)) = (9)/(20) = 0.45`

Sample percentage measurements estimated stdev

`= \sqrt{([(0.45)(1-0.45)])/([(16+4)])}\\\\ = \sqrt{([(0.45)(0.55)])/([(20)])}\\\\ = \sqrt{(0.2475)/(20)}\\\\= √(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 * 1.64 \\\\= 0.45 \pm 0.18204`