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 19 specimens of a particular species, 7 resprouted after fire. Estimate with 99.8% confidence the proportion of all shrubs of this species that will resprout after fire.

Interval:

Answer 1

Significance level = 1 = 0..998 = 0.002

From Z table, z critical value Z/2 = Z_0.001 = 3.0902

Sample proportion = 7 / 19 = 0.368

99.8% confidence interval for p is

- Z/2 sqrt [ ( 1 - ) / n ] < p < + Z/2 sqrt [ ( 1 - ) / n ]

0.368 - 3.0902 * sqrt(0.368 * ( 1 - 0.368 ) / 19 ) < p < 0.368 + 3.0902 * sqrt(0.368 * ( 1 - 0.368 ) / 19 )

0.026 < p < 0.710

99.8% CI is ( 0.026 , 0.710 )