Comprehensive and Detailed In-Depth

A95% confidence intervalis a statistical range, derived from sample data, that is likely to contain the true population mean. It reflects the degree of uncertainty or certainty in a sampling method.

Option C:A set of ranges contains the population mean with 95% certainty.

Rationale:This statement accurately describes a 95% confidence interval. It means that if we were to take 100 different samples and compute a confidence interval for each sample, we would expect about 95 of the intervals to contain the true population mean.

Option A:There is a 95% probability that a sample is within one standard deviation of the mean.

Rationale:This statement confuses confidence intervals with standard deviation. A 95% confidence interval pertains to the range within which the population mean is expected to lie, not the dispersion of individual sample points around the mean.

Option B:A stated range may contain 95% of the population mean, 95% of the time.

Rationale:This statement is incorrect because the population mean is a single value, not something that can be 95%