Respuesta :
With a 95% confidence interval, the proportion of all shrubs of this species that will resprout after a fire is between 0.17 and 0.67.
What is a confidence interval?
An area surrounding a measurement that indicates how accurate it is called a confidence interval.
Here, we have
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 the 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 = 14
x = 6
p = 6/14 = 0.42
q = 1 - 0.42 = 0.58
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail.
Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 2.05. Thus, Thus, the z score for a confidence level of 95% is 1.96
Therefore, the 95% confidence interval is
0.42 ± 1.96√(0.58)(0.42)/14
The lower limit of the confidence interval is
0.42 - 0.25 = 0.17
The upper limit of the confidence interval is
0.42 + 0.25 = 0.67
Hence, with a 95% confidence interval, the proportion of all shrubs of this species that will resprout after a fire is between 0.17 and 0.67.
To learn more about the confidence interval from the given link
https://brainly.com/question/20309162
#SPJ4
