The 2012 National Health and Nutrition Examination Survey reports a 95% confidence interval of 99.8 to 102.0 centimeters for the mean waist circumference of adult women in the United States.

a) What is captured by the confidence interval?

b) Express this confidence interval as a sequence written in the context of this problem.

c) What is the margin of error for this confidence interval? Express this interval in the format "estimate plus or minus margin of error."

d) Would a 99% confidence interval based on the same data be larger or smaller? Explain.

A confidence interval is a statistical range of values that is used to estimate an unknown population parameter, such as the mean or standard deviation of a distribution, based on a sample of data.

a) The confidence interval captures the plausible range of values for the population mean waist circumference of adult women in the United States. More specifically, it is the range of values that is likely to contain the true population mean with 95% confidence.

b) The confidence interval can be expressed as: "We are 95% confident that the true population mean waist circumference of adult women in the United States falls between 99.8 and 102.0 centimeters."

c) The margin of error for this confidence interval can be calculated by taking half the width of the interval. Therefore, the margin of error is (102.0 - 99.8) : 2 = 1.1. Thus, we can express the confidence interval as "The estimate is 100.9 centimeters plus or minus 1.1 centimeters."

d) A 99% confidence interval based on the same data would be larger than the 95% confidence interval. This is because a 99% confidence level requires a wider interval to capture the true population mean with 99% confidence.

Therefore, the interval would be wider, with more plausible values, and the margin of error would be larger.

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