Question

cases of Thirty-five small communities in Connecticut (population near 10,000 each) gave an average of x larceny per year. Assume that ơ is known to be 41.5 cases per year. 138.5 reported (a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit 126.96 (15004 upper limit 50.04 margin of error (b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit 2475 upper limit 152.25 margin of ewor (c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit ( 120 43 upper limit (150 57 margin of error (d) Compare the margins of error for parts (a) through (C). As the confidence levels increase, do the margins of error increase? O As the confidence level increases, the margin of error increases. O As the confidence level increases, the margin of error decreases OAs the confidence level increases, the margin of error remains the same. (e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels in crease, do the confidence intervals increase in length? O As the confidence level increases, the confidence interval increases in length. O As the confidence level increases, the confidence interval decreases in length

Answer 1

Answer

(A)We know that the formula for margin of error is given as

ME =

in this case, z = 1.64 for 90% (using z distribution table), n = sample size = 35 and

setting the values, we get

ME =

So, required margin of error = 11.50(rounded to 2 decimals) or 11.5 (rounded to one decimal)

(B) We know that the formula for margin of error is given as

ME =

in this case, z = 1.96 for 95% (using z distribution table), n = sample size = 35 and

setting the values, we get

ME =

So, required margin of error = 13.75(rounded to 2 decimal) or 13.7(rounded to one decimal)

All other answers are arleady correct