Question: FBI Report . Thirty small communities in Connecticut (population near 10,000 each) gave an average of \(\bar{X}\) = 138.5 reported cases of larceny per year.

Assume that \(\sigma \) is known to be 42.6 cases per year (Reference: Crime in the United

States, Federal Bureau of Investigation).

1. Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
2. Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
3. Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
4. Compare the margins of error for parts (a) through (c). As the confidence level increases, does the margin of error increase?

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the
confidence level increases, does the confidence interval increase in length?

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