A civil engineer tested concrete samples to investigate the difference in strength, in newtons per square millimeter (N/mm2), 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.

Question

28-04-2020
Mathematics

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A civil engineer tested concrete samples to investigate the difference in strength, in newtons per square millimeter (N/mm2), 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.

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Favouredlyf Favouredlyf · Answer 1 · 2020-05-03T03:43:49+02:00

Answer: 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.

Step-by-step explanation:

Confidence interval is constructed to estimate a range of values that could possibly contain the population parameter. This could be the population mean or population proportion. A 95 percent confidence interval does not mean 95% probability. It tells how confident that we are that the confidence interval contains the population proportion. If we construct 100 of the given confidence interval, we are confident that 95% of them would contain the true population parameter. Therefore, the correct option is

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.

tallinn tallinn · Answer 2 · 2022-04-04T09:56:22+02:00

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.

What is Probability?

A confidence interval is constructed to evaluate a range of significances that could incorporate the population parameter. This could be the population compromise or population proportion. A 95 percent confidence interval does not indicate a 95% probability. It describes how confident we are that the confidence interval includes the population proportion. If we construct 100 of the shared confidence interval, we are confident that 95% of them would include the true population parameter. Thus, the correct option is 'D'. In repeated illustrations of the same size, approximately 95 percent of the intervals constructed from the samplings will capture the population distinction in norms.

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