Final answer:
The probability that a range includes the true population parameter is known as the confidence level. A confidence interval is constructed around the point estimate with an error bound known as the margin of error, which varies depending on the chosen confidence level.Option 3 is the correct answer.
Step-by-step explanation:
The probability that a specified range contains the true population value is called the confidence level. When constructing a confidence interval (CI) for an unknown population mean, point estimates such as the sample mean (x) and the sample standard deviation (s) are utilized to estimate the population parameters. In the case that the population standard deviation (σ) is known, the error bound for the population mean (EBM) can be calculated, which is also known as the margin of error. The CI is expressed as an interval of values formed around the point estimate and factoring in the margin of error. The confidence interval has the general form (point estimate - EBM, point estimate + EBM).
For example, if we are calculating the confidence interval for a population mean with a known standard deviation and our sample has a mean of x = 10, with a 90% confidence interval (5, 15), the margin of error would be 5. If the confidence level is 95%, and the CI is (4.5, 9.5), we estimate with 95 percent confidence that the true population mean lies between those two numbers.
The confidence interval gives a range that the true population parameter is likely contained within, based on our sample data and chosen confidence level. This range accounts for sampling variability and is not the same as the standard error of the mean, which is a measure of the precision of the sample mean estimate alone.