Which of the following is a correct statement about a 90 con

Which of the following is a correct statement about a 90% confidence interval?

If we repeatedly draw samples of the same size from the same population and construct confidence interval at the 90% confidence level using each sample mean, 90% of the resulting confidence intervals will include m.

There is a 90% probability that the population mean m will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL).

We are 90% confident that our sample mean equals the population mean m.

d 90% of the population values will lie within the confidence interval.

Solution

Which of the following is a correct statement about a 90% confidence interval?

a

If we repeatedly draw samples of the same size from the same population and construct confidence interval at the 90% confidence level using each sample mean, 90% of the resulting confidence intervals will include m.

b

There is a 90% probability that the population mean m will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL).

c

We are 90% confident that our sample mean equals the population mean m.

d 90% of the population values will lie within the confidence interval.

If we sample data from the population of interest then the prescription we use to calculate the upper and lower limits of the confidence interval will produce an interval that will include the true (unknown) population parameter in 90% of the samples that are possible to draw. Therefore 10% of the possible samples would not include the parameter.