Which is true about a 99% confidence interval for a population proportion based on a given sample?
I. We are 99% confident that the population proportion is in our interval.
II. There is a 99% chance that our interval contains the sample proportion.
III. The interval is wider than a 95% confidence interval would be.
A) II only
B) I and III
C) I only
D) None are true
E) III only
F) II and II
I think the answer would be E...
I would say B.
To determine the correct answer, let's analyze each option:
I. "We are 99% confident that the population proportion is in our interval."
This statement is true for a confidence interval. A 99% confidence interval means that if we were to repeat the sampling process and construct intervals in the same way, approximately 99% of those intervals would contain the true population proportion. Therefore, option I is true.
II. "There is a 99% chance that our interval contains the sample proportion."
This statement is incorrect. The confidence interval provides a range of plausible values for the population proportion, but it does not imply a probability or chance. It is either the case that the true population proportion is in the interval or it is not. Option II is false.
III. "The interval is wider than a 95% confidence interval would be."
This statement is true. A higher confidence level leads to a wider interval. This is because a higher confidence level involves reducing the margin of error and capturing a larger range of possible values. Thus, option III is true.
Based on our analysis, the correct answer is B) I and III.