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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.