Certified Internal Auditor (CIA) Practice Test

What does a 90% confidence interval for the mean of a population imply?

1. Estimate is equal to the true population mean.

2. True population mean is no larger than the largest endpoint of the interval.

3. Standard deviation will not be greater than 10% of the population mean.

4. True population mean lies within the specified confidence interval.

The correct answer is: True population mean lies within the specified confidence interval.

A 90% confidence interval for the mean of a population indicates that if you were to collect many random samples and compute a confidence interval from each sample, approximately 90% of those intervals would contain the true population mean. Consequently, this means there is a high degree of certainty (90%) that the true population mean lies within the boundaries established by the confidence interval calculated from the sample data. This concept stems from the principles of inferential statistics and the behavior of sampling distributions. The confidence interval reflects both the variability of the sample data and the degree of confidence chosen by the researcher. Thus, asserting that the true population mean lies within this specified range is a direct interpretation of what the confidence interval represents. In contrast, the other options do not accurately describe the implications of a 90% confidence interval. Estimating the mean as equal to the true population mean overlooks the inherent uncertainty involved. Claiming that the true mean is no larger than the largest endpoint of the interval ignores the fact that the mean could also be smaller than the lower endpoint. Finally, stating that the standard deviation will not be greater than 10% of the population mean relates to a different aspect of statistical analysis and isn’t a characteristic of the confidence interval.