Chapter 8.1, Problem 23E

To determine

The correct statement that gives a valid interpretation for the confidence interval

(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)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.

Answer to Problem 23E

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

Explanation of Solution

Given Information:

Selected employees = 25

Confidence interval = 95%

Mean systolic blood pressure $=\left(\text{122},\text{138}\right)$

In option (a) the confidence interval gives only the information about the mean of the population. Thus, option (a) is incorrect.

In option (b) the confidence interval gives only the information about the mean of the population. Thus, option (b) is incorrect.

In option (c) since the confidence interval of 95% contain the true mean of all possible samples. Thus, option (c) is correct.

There is no information on probability is given in option (d). Thus, option (d) is incorrect.

In option (e) center of the confidence interval may not be the true mean. Thus, option (e) is incorrect.

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