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7 October, 04:56

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, 6 resprouted after fire. Estimate with 96% confidence the proportion of all shrubs of this species that will resprout after fire. Interval:.1884 to

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  1. 7 October, 07:11
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    Step-by-step explanation:

    Confidence interval is written as

    Sample proportion ± margin of error

    Margin of error = z * √pq/n

    Where

    z represents the z score corresponding to the confidence level

    p = sample proportion. It also means probability of success

    q = probability of failure

    q = 1 - p

    p = x/n

    Where

    n represents the number of samples

    x represents the number of success

    From the information given,

    n = 19

    x = 6

    p = 6/19 = 0.32

    q = 1 - 0.32 = 0.68

    To determine the z score, we subtract the confidence level from 100% to get α

    α = 1 - 0.96 = 0.04

    α/2 = 0.04/2 = 0.02

    This is the area in each tail. Since we want the area in the middle, it becomes

    1 - 0.02 = 0.98

    The z score corresponding to the area on the z table is 2.05. Thus, Thus, the z score for a confidence level of 96% is 2.05

    Therefore, the 96% confidence interval is

    0.32 ± 2.05√ (0.68) (0.32) / 19

    The lower limit of the confidence interval is

    0.32 - 0.22 = 0.1

    The upper limit of the confidence interval is

    0.32 + 0.22 = 0.54

    Therefore, with 96% confidence interval, the proportion of all shrubs of this species that will resprout after fire is between 0.1 and 0.54
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