Under a valid 95% frequentist confidence procedure for a population mean, what does the confidence level describe?
Correct Answer
B) About 95% of intervals from repeated samples would contain the fixed population mean
A 95% frequentist confidence procedure, under its assumptions, produces intervals containing the fixed population mean in 95% of repeated samples. A realized interval describes estimation uncertainty; it does not contain every individual sale, measure the probability of unbiased sampling or count buyer agreement. Its nominal coverage can fail when sampling or model assumptions are inappropriate.
Why This Is the Correct Answer
Option B is correct because a valid 95% confidence procedure, under its assumptions, produces intervals that would contain the fixed population mean in about 95% of repeated samples. The population mean is fixed and the intervals vary from sample to sample. Nominal coverage can fail if sampling or model assumptions are inappropriate.
Why the Other Options Are Wrong
Option A: Each individual sale price in the sample falls within the realized 95% confidence interval
Option A claims each individual sale price falls within the realized 95% confidence interval, which is wrong. A confidence interval for the mean describes estimation uncertainty about the mean, not the spread of individual sales, many of which can fall outside it.
Option C: The sample has a 95% probability of being unbiased
Option C says the sample has a 95% probability of being unbiased, but the confidence level does not measure the probability of unbiased sampling. A biased sample can undermine the coverage the procedure is meant to deliver.
Option D: About 95% of buyers agree with the estimated mean
Option D says about 95% of buyers agree with the estimated mean, which confuses a statistical coverage rate with an opinion poll. Confidence level has nothing to do with buyer agreement.
Procedure, not the point
The 95% describes how often the interval-making procedure succeeds over many samples, not anything about individual sales.
How to use: Use this when a question asks what a confidence level means.
Exam Tip
Look for the answer that mentions repeated samples and the population parameter; reject answers about individual data points or opinions.
Common Mistakes to Avoid
- -Thinking individual observations fall inside the confidence interval
- -Interpreting the confidence level as the probability the sample is unbiased
- -Treating the population mean as random and the interval as fixed
Concept Deep Dive
Analysis
This question tests the correct frequentist interpretation of a confidence level. The 95% refers to the long-run performance of the procedure: across many repeated samples, about 95% of the resulting intervals would contain the fixed population mean. It does not describe individual observations, bias probability or opinions.
Background Knowledge
A confidence interval gives a range of plausible values for a population parameter based on sample data. The confidence level describes how often the procedure captures the true parameter over repeated sampling. Narrower intervals generally come from larger samples or less variable data.
Real-World Application
A ratio study reports a 95% confidence interval for the mean ratio of 0.94 to 1.00. An analyst explains that the method used would capture the true population mean in about 95% of repeated samples, while many individual ratios fall outside that interval.
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