You have measured the systolic blood pressure of an SRS of...

You have measured the systolic blood pressure of an SRS of 25 company employees. A $95 \%$ confidence interval for the mean systolic blood pressure for the employees of this company is $(122,138) .$ Which of the following statements is true? (a) $95 \%$ of the sample of employees have a systolic blood pressure between 122 and 138 . (b) $95 \%$ of the population of employees have a systolic blood pressure between 122 and 138 . (c) If the procedure were repeated many times, $95 \%$ of the resulting confidence intervals would contain the population mean systolic blood pressure. (d) If the procedure were repeated many times, $95 \%$ of the time the population mean systolic blood pressure would be between 122 and 138 . (e) If the procedure were repeated many times, $95 \%$ of the time the sample mean systolic blood pressure would be between 122 and 138 .

You have measured the systolic blood pressure of an SRS of 25 company employees. A $95 \%$ confidence interval for the mean systolic blood pressure for the employees of this company is $(122,138) .$ Which of the following statements is true?
(a) $95 \%$ of the sample of employees have a systolic blood pressure between 122 and 138 .
(b) $95 \%$ of the population of employees have a systolic blood pressure between 122 and 138 .
(c) If the procedure were repeated many times, $95 \%$ of the resulting confidence intervals would contain the population mean systolic blood pressure.
(d) If the procedure were repeated many times, $95 \%$ of the time the population mean systolic blood pressure would be between 122 and 138 .
(e) If the procedure were repeated many times, $95 \%$ of the time the sample mean systolic blood pressure would be between 122 and 138 .

Key Concepts

Confidence Interval

A confidence interval is a range constructed from sample data that is believed, with a certain confidence level (typically 95%), to contain the true population parameter. It is calculated using the sample statistic and its associated variability, and its interpretation is based on the long-run performance of the procedure used to generate it.

Repeated Sampling

Repeated sampling refers to the process of taking many independent samples from the same population. In the context of confidence intervals, it means that if the same method of constructing the interval is applied to many samples, a specified proportion (e.g., 95%) of those intervals will contain the actual population parameter.

Parameter vs. Statistic

This concept distinguishes between a population parameter, which is a fixed but unknown value, and a sample statistic, which is a random variable computed from the data. Confidence intervals are built around sample statistics, acknowledging that while the interval is random, the population parameter is static.

Misinterpretations of Confidence Intervals

Common errors in interpreting confidence intervals include confusing the interval for the range of individual data values, assuming that a specific interval has a fixed probability of containing the parameter after the data are observed, or mistaking the confidence level as pertaining to the proportion of the population falling within the interval. Correct interpretation involves understanding the long-run frequency with which intervals constructed from repeated samples contain the true parameter.

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