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. 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.

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Chapter1: Combinatorial Analysis
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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. 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 as illustrated in Example 23.6

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