Question
10. Suppose twenty-seven communities have an average of x=133.5 reported cases of larceny per year. Assume that standard deviation is known to be 41.7 cases
10. Suppose twenty-seven communities have an average of x=133.5 reported cases of larceny per year. Assume that standard deviation is known to be 41.7 cases per year. Find an 80%, 90%, and 95% confidence interval for the population mean annual number of reported larceny cases in such communites. Compar the lenfths of the confidence intervals. As the confidence levels increase, do the confidence intervals increase in length?
A) The 80% confidence level has a confidence interval length of 106.8; the 90% confidence level has a confidence interval length of 137.2; and the 95% confidence level has a confidence interval length of 163.5. As the confidence level increases, the confidence interval length increases.
B) The 80% confidence level has a confidence interval length of 6.1; the 90% confidence level has a confidence interval length of 5.1; and the 95% confidence level has a confidence interval length of 4.0; As the confidence level increases, the confidence interval length decreases.
c) The 80% confidence level has a confidence interval length of 20.5; the 90% confidence level has a confidence interval length of 26.4; and 95% confidence level has a confidence interval length of 31.5. As the confidence level increases, the confidence interval lengths increases.
d) The 80% confidence level has a confidence interval length of 4.0; the 90% confidence level has a confidence interval length of 5.1; and the 95% confidence level has a confidence interval length of 6.1. As the confidence level increases, the confidence interval lengths increases.
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