A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?
A) 95% of the sample of employees has a systolic blood pressure between 123 and 139.
B) If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
C) 95% of the population of employees has a systolic blood pressure between 123 and 139.
D) If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.

Question

A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?
A) ​95% of the sample of employees has a systolic blood pressure between 123 and 139.
B) ​If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
C) ​95% of the population of employees has a systolic blood pressure between 123 and 139.
D) ​If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.

Quizplus · Accepted Answer

The 95% confidence interval means that if we were to repeat the sampling procedure and construct a confidence interval each time, we would expect 95% of those intervals to contain the population mean systolic blood pressure. This statement describes the concept of "confidence" in a confidence interval. Options A and C are incorrect because they incorrectly interpret the confidence interval as applying to the sample or the population as a whole, respectively. Option D is incorrect because it refers to the specific sample mean, whereas the confidence interval pertains to the population mean.

A Random Sample of 25 Employees of a Local Company