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? (This is a multiple-select question; you must choose all of the correct choices and none of the incorrect choices to receive credit for this question.) Note: 6 submissions allowed.

-95% of the sample of employees have a systolic blood pressure between 142 and 165.

-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 142 and 165.

-95% of the population of employees have a systolic blood pressure between 142 and 165.

-We are 95% confident that the population mean systolic blood pressure μ of all employees is in the interval (142, 165).

-We are 95% confident that the interval (142, 165) contains the population mean systolic blood pressure μ of all employees.

-The probability that the population mean systolic blood pressure μ is between 142 and 165 is .95.

-On 95% of the days the population mean systolic blood pressure μ is between 142 and 165.

-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 μ; (142, 165) is one such interval.

-We are 95% confident that the systolic blood pressures in this sample have a sample mean that is between 142 and 165.

Answer 1

The answers are:

We are 95% confident that the interval (142, 165) contains the population mean systolic blood pressure μ of all employees.

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 μ; (142, 165) is one such interval.

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