Shrubs that Withstand Fire Fire is a serious threat to shru

Shrubs that Withstand Fire . Fire is a serious threat to shrubs in dry climates.Some shrubs can resprout from their roots after their tops are destroyed. One study of resprouting took place in a dry area of Mexico.¹³ The investigators first clipped the tops of all the shrubs in the study. For the treatment, they then applied a propane torch to the stumps of the shrubs to simulate a fire, and for the control the stumps were left alone. The study included 24 shrubs of which 12 were randomly assigned to the treatment and the remaining 12 to the control. A shrub is a success if it resprouts. For the shrub Xerospirea hartwegiana, all 12 shrubs in the control group resprouted, whereas only 8 in the treatment group resprouted. How much does burning reduce the proportion of shrubs of this species that resprout? Give the 95% plus four confidence interval for the amount by which burning reduces the proportion of shrubs of this species that resprout. The plus four method is particularly helpful when, as here, a count of either successes or failures is zero.Follow the four-step process

Solution

Plus Four Confidence Interval
CI = p ± Z a/2 Sqrt(p*(1-p)/n+4)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=8
Sample Size(n)=12
Sample proportion = x+2/n+4 =0.625
Confidence Interval = [ 0.625 ±Z a/2 ( Sqrt ( 0.625*0.375) /16)]
= [ 0.625 - 1.96* Sqrt(0.0146) , 0.625 + 1.96* Sqrt(0.0146) ]
= [ 0.3878,0.8622]