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, 5 resprouted after fire. Estimate with 95% confidence the proportion of all shrubs of this species that will resprout after fire.

Interval:  to

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 5 / 16 = 0.3125

1 - = 1 - 0.3125 = 0.6875

Z/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.3125 * 0.6875) / 16)

= 0.227

A 95% confidence interval for population proportion p is ,

± E  

= 0.3125  ± 0.227

= ( 0.086, 0.540 )

confidence interval = 0.086 to 0.540