Question

An 85% confidence interval for the parameter of interest was

found to be (0.004, 0.019) using bootstrapping methods. Interpret
this interval in the context of the problem. Be sure to note which
group

Answer 1

An 85% confidence interval from bootstrapping suggests we can be 85% confident that the true population parameter lies within (0.004, 0.019). The confidence interval does not contain 85% of the data but rather indicates the reliability of the interval to contain the true parameter if the estimation were repeated. Wider confidence intervals imply higher certainty that they contain the true value of the parameter.

Step-by-step explanation:

The question refers to the interpretation of a confidence interval that was obtained using bootstrapping methods. A confidence interval provides a range of values that is likely to contain the parameter of interest—in this case, likely a mean, proportion, or difference between means—of the entire population from which the sample was taken. With an 85% confidence interval of (0.004, 0.019), we can say we are 85% confident that the true parameter of interest lies within this interval. However, this does not mean that 85% of the data lies within this interval, but rather that the procedure used to calculate this interval would produce intervals that contain the true parameter 85% of the time if we repeated the process many times.

As confidence intervals relate to the reliability of estimating a population parameter, higher confidence levels—such as 90% or 95%—yield wider intervals. Wider intervals reflect more certainty that they contain the true value, and is why a 95% confidence interval is wider than a 90% confidence interval, as more probability is covered. It's important to note that while bootstrapping is a resampling technique used to estimate statistics on a population by sampling a dataset with replacement, the confidence interval thus obtained still represents the same concept of range of plausible values for a population parameter.

Answer 2

The 85% confidence interval (0.004, 0.019) means we are 85% confident that the true parameter of interest lies between these values. This doesn't mean there's an 85% chance this particular interval contains the parameter; rather, it reflects the reliability of the interval-creating method (bootstrapping) over many samples.

Step-by-step explanation:

The 85% confidence interval you've provided, (0.004, 0.019), indicates with 85% confidence that the true parameter of interest, which could be a population mean or proportion, lies between 0.004 and 0.019. The interpretation of this interval is that if we were to take many samples and build a confidence interval from each sample using the same method (bootstrapping), we expect that 85% of those intervals would contain the true parameter.

It's important to note that this does not mean there is an 85% probability that the specific interval (0.004, 0.019) contains the true parameter; the confidence level only describes the long-run success rate of the method used to construct the confidence interval. The group that these statistics are about is not specified in your question, but it would refer to the population from which the sample was drawn to conduct the analysis.