Question

Dewey, Lie, and Howe is a regional branch office of the tax preparation conglomerate Hookem, Billem, Cheatem, and Soakem. One week before the deadline for filing federal income tax returns, the systolic blood pressure of a random sample of 45 employees at Dewey, Lie, and Howe is measured. Based on the observations in this sample, a 95% confidence interval for the mean systolic blood pressure μ of all employees is calculated to be (142, 165). Which of the following statements give a statistically correct, acceptable interpretation of this interval?

a. 95% of the sample of employees have a systolic blood pressure between 122 and 138.
b. We are 95% confident that the interval (122, 138) contains the population mean systolic blood pressure of all employees.
c. If the sampling procedure were repeated many times and the sample mean systolic blood pressure from the observations in each sample were calculated, then 95% of the sample means would be between 122 and 138.
d. The probability that the population mean systolic blood pressure is between 122 and 138 is .95.
e. 95% of the population of employees have a systolic blood pressure between 122 and 138.
f. If the sampling procedure were repeated many times and a 95% confidence interval calculated from the observations in each sample, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure ; (122, 138) is one such interval.
g. We are 95% confident that the population mean systolic blood pressure of all employees is in the interval (122, 138).
h. We are 95% confident that the systolic blood pressures in this sample have a sample mean that is between 122 and 138. On 95% of the days the population mean systolic blood pressure is between 122 and 138.

Answer 1

Answer:

b. We are 95% confident that the interval (122, 138) contains the population mean systolic blood pressure of all employees.

g. We are 95% confident that the population mean systolic blood pressure of all employees is in the interval (122, 138).

Step-by-step explanation:

The confidence interval of the question is not coincident with the confidence interval of the answers option.

A confidence interval is a range of values for which we estimate, with a certaing degree of confidence, that a certain parameter of the population is within this interval.

In this case, with the interval of (122, 138), we are 95% confident that the real population mean systolic blood pressure is within 122 and 138.

The interval is calculated from the information extracted of a sample, but it infers something about a parameter of the population.

It does not infer about the probabilities of individual values or sample statistic.

Then, according to this interpretation, the correct answers are:

b. We are 95% confident that the interval (122, 138) contains the population mean systolic blood pressure of all employees.

g. We are 95% confident that the population mean systolic blood pressure of all employees is in the interval (122, 138).