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A researcher selects a random sample of size n from a population and uses the collected data to compute a 95% confidence interval for the mean of the

population. If the same data were used to compute a second confidence interval, which of the following produces a confidence interval with a larger margin
of error?

User Erosebe
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Final answer:

A 99% confidence interval will have a larger margin of error than a 95% confidence interval because it provides a higher level of certainty by including more of the population's data points. The confidence level is directly proportional to the margin of error.

Step-by-step explanation:

A researcher selecting a random sample to compute a 95% confidence interval for the mean of the population may be considering whether the confidence interval would be wider if the confidence level was increased. A confidence interval's margin of error will increase if the confidence level is increased. For instance, a 99% confidence interval will be wider than a 95% confidence interval, because it aims to capture more of the population's data points, thus providing a higher confidence in capturing the true population mean.

Confidence level is directly proportional to the margin of error, as higher confidence levels reflect greater certainty and consequently require a wider interval to capture the true population mean. A smaller sample size also contributes to a larger margin of error due to increased variability within the sample.

As such, if one were to compute a second confidence interval from the same data and wanted a larger margin of error, they would have to opt for a higher confidence level, such as 99%, because this would incorporate more of the normal distribution's area, leading to a broader range.

User Oleh Dokuka
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