Some shrubs have the useful ability to resprout from their roots after their top

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 14 specimens of a particular species, 7 resprouted after fire. Estimate with 95% confidence the proportion of all shrubs of this species that will resprout after fire.

Explanation / Answer

Confidence Interval:

p^ (-/+) E

p^ = 7/14 = 0.5

E = zc * sqrt (p^*(1-p^))/n)

zc is the critical value at 5% level of significance. From normal table we get this value as 1.96

E = 1.96 * sqrt ((0.5*(1-0.5))/14)

= 0.262

P^ (-/+) E

0.5 (-/+) 0.262

0.238 and 0.762

Answer: The 95% confidence interval is 0.238 and 0.762

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