An environmental organization wants to estimate the proportion of trees that are
ID: 3362236 • Letter: A
Question
An environmental organization wants to estimate the proportion of trees that are diseased in a particular forest. A preliminary result from random sampling showed that 8.32% of the trees are diseased and produced the following 95% confidence interval: (0.0605, 0.1059). What is the correct interpretation of this interval?
Question options:
A There is a 95% chance that 8.32% of the trees are diseased.
B There is a 95% chance that the sample proportion will fall in the interval 6.05% and 10.59%.
C 95% of the time the true proportion will fall in the interval (0.0605, 0.1059).
D 95% of the time the procedure used will create an interval that contains the true proportion, thus we are 95% confident that the interval (0.0605, 0.1059) contains the true proportion.
E 95% of the time the randomly selected samples will show a proportion that is in the interval (0.0605, 0.1059).
F None of the above choices
A There is a 95% chance that 8.32% of the trees are diseased.
B There is a 95% chance that the sample proportion will fall in the interval 6.05% and 10.59%.
C 95% of the time the true proportion will fall in the interval (0.0605, 0.1059).
D 95% of the time the procedure used will create an interval that contains the true proportion, thus we are 95% confident that the interval (0.0605, 0.1059) contains the true proportion.
E 95% of the time the randomly selected samples will show a proportion that is in the interval (0.0605, 0.1059).
F None of the above choices
Explanation / Answer
The correct answer is:
E 95% of the time the randomly selected samples will show a proportion that is in the interval (0.0605, 0.1059).
This goes by the definition of confidence level of an interval.