What is the probability that the interval estimate will include the population parameter?

What is the probability that the interval estimate will include the population parameter?

• A. Point Estimate
• B. Confidence Level
• C. Confidence Interval
• D. Margin of Error

Answer: (B)

The idea being tested is how we express the likelihood that our interval really captures the true population value. The probability that the interval estimate will include the population parameter is called the confidence level. It’s usually given as a percentage, like 95% or 99%, and it refers to the long-run performance of the interval method: if we repeated the sampling many times and built an interval each time, about that percentage of those intervals would contain the true parameter. For a single sample, the interval either does or does not contain the parameter; the confidence level describes how often this would happen across many repetitions of the study. A higher confidence level means we’re more likely to include the parameter, but the interval becomes wider, reducing precision. A lower confidence level makes the interval narrower and more precise but less likely to contain the true value. To contrast the terms: a point estimate is just the single best guess of the parameter. A confidence interval is the range around that guess that we’re confident, at a specified level, contains the parameter. The margin of error is the amount added and subtracted from the point estimate to form that interval—the half-width of the interval.

The idea being tested is how we express the likelihood that our interval really captures the true population value. The probability that the interval estimate will include the population parameter is called the confidence level. It’s usually given as a percentage, like 95% or 99%, and it refers to the long-run performance of the interval method: if we repeated the sampling many times and built an interval each time, about that percentage of those intervals would contain the true parameter.

For a single sample, the interval either does or does not contain the parameter; the confidence level describes how often this would happen across many repetitions of the study. A higher confidence level means we’re more likely to include the parameter, but the interval becomes wider, reducing precision. A lower confidence level makes the interval narrower and more precise but less likely to contain the true value.

To contrast the terms: a point estimate is just the single best guess of the parameter. A confidence interval is the range around that guess that we’re confident, at a specified level, contains the parameter. The margin of error is the amount added and subtracted from the point estimate to form that interval—the half-width of the interval.