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 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 $122\mathrm{and}138$.

Short answer

The correct option is (c).

Step-by-step solution

Given Information

It is given that $95\%$interval for mean systolic pressure is$(122,138)$.

Explanation

It means that it is $95\%$assured that $95\%$of samples have $95\%$confidence interval that has correct population parameter.

If process is repeated several times, $95\%$of confidence intervals contain population mean systolic pressure.

Option (c) is correct.