Suppose thirty-nine communities have an average ofx=142.1reported cases of larceny per year. Assume thatis known to be 46.9 cases per year. Find a 90%, 95%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the lengths of the confidence intervals. As the confidence levels increase, do the confidence intervals increase in length?

Group of answer choices

The 90% confidence level has a confidence interval length of 24.7; the 95% confidence level has a confidence interval length of 29.4; and the 98% confidence level has a confidence interval length of 35.0. As the confidence level increases, the confidence interval lengths increases.

The 90% confidence level has a confidence interval length of 5.6; the 95% confidence level has a confidence interval length of 4.7; and the 98% confidence level has a confidence interval length of 4.0. As the confidence level increases, the confidence interval length decreases.

The 90% confidence level has a confidence interval length of 218.6; the 95% confidence level has a confidence interval length of 183.8; and the 98% confidence level has a confidence interval length of 154.3. As the confidence level increases, the confidence interval lengths decreases.

The 90% confidence level has a confidence interval length of 4.0; the 95% confidence level has a confidence interval length of 4.7; and the 98% confidence level has a confidence interval length of 5.6. As the confidence level increases, the confidence interval lengths increases.

The 90% confidence level has a confidence interval length of 154.3; the 95% confidence level has a confidence interval length of 183.8; and the 98% confidence level has a confidence interval length of 218.6. As the confidence level increases, the confidence interval length increases.