Probability, Statistics and Queueing
Which of the following correctly describes the meaning of a 95% confidence interval for the population mean obtained from a sample?
- AIt means that about 95% of the individual values in the population lie within the interval
- BIf samples were drawn again and intervals computed by the same method many times, about 95% of the intervals would contain the population mean
- CThe larger the sample, the more variation it contains, so the interval at the same confidence level becomes wider
Show answer and explanation
Answer: B. If samples were drawn again and intervals computed by the same method many times, about 95% of the intervals would contain the population mean
A confidence interval estimates an unknown value, such as the population mean, from a sample with a range. A 95% confidence interval is an interval made by a method such that, if sampling were repeated, about 95% of the resulting intervals would contain the true population mean. The width of the interval is proportional to the standard error σ/√n, so it narrows as the sample grows.
- A. It shows the range of the estimate of the population mean, not the spread of individual values. The range containing about 95% of the individual values is the mean ±about 2σ, which is much wider.
- B. Correct. It expresses that the method of making the interval contains the population mean about 95% of the time when repeated.
- C. The width of the interval is proportional to σ/√n, so it narrows as the sample grows.
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