Question

A civil engineer tested concrete samples to investigate the difference in strength, in newtons per square millimeter (N/mm^2), between concrete hardened for 21 days and concrete hardened for 28 days. The engineer measured the strength from each sample, calculated the difference in the mean strength between the samples, and then constructed the 95 percent confidence interval, (2.9,3.1), for the difference in mean strengths.Assuming all conditions for inference were met, which of the following is a correct interpretation of the 95 percent confidence level?a) In repeated samples of the same size, approximately 95 percent of the samples will yield the interval 2.9 N/mm^2 to 3.1 N/mm^2.b) In repeated samples of the same size, approximately 95 percent of the sample means will fall between 2.9 N/mm^2 and 3.1 N/mm^2.c) In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will extend from 2.9 N/mm^2 to 3.1 N/mm^2.d) In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means.e) In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the sample difference in means.

Answer 1

e) In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the sample difference in means.

Explanation:

We have a 95% confidence interval for the difference that is (2.9, 3.1).

All conditions for inference are assumed to be met.

The confidence interval for the difference will give us a interval within we expect to find the true difference with the degree of confidence that the interval was calculated.

In this case, we are 95% confident that the true difference between the strength of the concrete hardened for 28 days and the concrete hardened fo 21 days is within 2.9 N/mm^2 and 3.1 N/mm^2.

The meaning of the confidence level for multiple samples is that, if we get repeated samples of the same size, 95% (in this case) of the confidence interval constructed from that samples will contain the true difference.

Therefor, the right option is e): "In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means."