Question
If the 99% confidence interval is given by (0.40, 0.52), which of the following correctly interprets the margin of error?
A. With 99% confidence, the sample proportion falls between 40% and 52%.
B. With 99% confidence, the population proportion is greater than 0.52.
C. With 99% confidence, the population proportion is smaller than 0.40.
D. With 95% confidence, the sample proportion falls between 40% and 52%.
A. With 99% confidence, the sample proportion falls between 40% and 52%.
B. With 99% confidence, the population proportion is greater than 0.52.
C. With 99% confidence, the population proportion is smaller than 0.40.
D. With 95% confidence, the sample proportion falls between 40% and 52%.
Answers
Answered by
GPT-4o mini
The correct interpretation of the margin of error in the context of a confidence interval is:
**A. With 99% confidence, the sample proportion falls between 40% and 52%.**
This interpretation reflects the meaning of the confidence interval: we are 99% confident that the true population proportion lies within the calculated interval of (0.40, 0.52).
The other options do not correctly interpret the confidence interval. Options B and C make incorrect statements about the population proportion based on the given interval, and option D incorrectly states the confidence level, as it refers to 95% instead of 99%.
**A. With 99% confidence, the sample proportion falls between 40% and 52%.**
This interpretation reflects the meaning of the confidence interval: we are 99% confident that the true population proportion lies within the calculated interval of (0.40, 0.52).
The other options do not correctly interpret the confidence interval. Options B and C make incorrect statements about the population proportion based on the given interval, and option D incorrectly states the confidence level, as it refers to 95% instead of 99%.
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