Question

The confidence intervals give both lower and upper bounds on plausible values for the population characteristic being estimated. In some instances, only an upper bound or only a lower bound is appropriate. When n is large, what is the confidence level for a two-sided confidence interval?

1) 90%
2) 95%
3) 99%
4) Cannot be determined

Answer 1

The confidence level for a large-sample two-sided confidence interval cannot be determined without more context. Choices such as 90%, 95%, or 99% reflect the proportion of the normal distribution covered and thus the certainty that the interval contains the true population parameter. The confidence interval is calculated using a point estimate and margin of error, which depends on the confidence level and the standard error.

Step-by-step explanation:

The confidence level for a two-sided confidence interval when n is large cannot be determined without additional information. The confidence level describes the probability that the interval contains the true population parameter. For instance, a 90% confidence interval includes the central 90% of the normal distribution and excludes 5% in each tail. A 95% confidence interval is wider as it excludes 2.5% from each tail, offering more certainty that the interval contains the true population mean. Finally, a 99% confidence interval is even wider, excluding only 0.5% from each tail, which increases the level of confidence.

For constructing a confidence interval (CI), the formula used is (point estimate – margin of error, point estimate + margin of error). The margin of error depends on the confidence level and the standard error of the mean.

Example:

If for a particular study, a 95% confidence interval for the mean is given as (4.5, 9.5), we can interpret it as "We are 95 percent confident that the true value of the population mean is between 4.5 and 9.5."