Q. 23 - The Practice of Statistics for AP

Question

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 gives a valid interpretation of this interval?

(a) $95\%$ of the sample employees have systolic blood pressure between $122 and 138$.

(b) $95\%$ of the population of employees have 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) The probability that the population mean blood pressure is between $122 and 138$ is 0.95.

(e) If the procedure were repeated many times, $95\%$ of the sample means would be between $122 and 138$. 

Step-by-Step Solution

Answer

(c) If the procedure were repeated many times, $95\%$ of the resulting confidence intervals would contain the population mean systolic blood pressure. 

Step 1: Given Information

Given in the question that, a $95\%$ confidence interval for the mean systolic blood pressure for the employees of this company is $(122, 138)$

Step 2: Explanation

(a) Incorrect, because the confidence interval gives information about the mean of the population, not of the individuals.

(b) Incorrect, because the confidence interval gives information about the mean of the population, not of the individuals.

(c) Correct, the confidence interval of $95\%$of all possible samples will contain the true population mean.

(d) Incorrect, because the confidence interval gives us no information on probability.

(e) Incorrect, this would only be true if the center of the confidence interval $95\%$ is the true population mean.