Question

# Thirty small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5...

Thirty small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 40.3 cases per year.

(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 upper limit 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 upper limit margin of error

(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 upper limit margin of error

Formula

Confidence Interval for population Mean When Population Standard deviation is known

Margin of error:

Given,

Sample average reported cases of larceny per year : Sample average : = 138.5

Population Standard deviation : = 40.3 cases per year

Sample Size : n= 30

(a)

for 90% confidence level = (100-90)/100 = 0.1

/2 = 0.05

Z/2 = Z0.05 = 1.6449

90% confidence interval for the population mean annual number of reported larceny cases in such communities

Margin of error

 lower limit 126.4 upper limit 150.6 margin of error 12.1

(b)

for 95% confidence level = (100-95)/100 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

95% confidence interval for the population mean annual number of reported larceny cases in such communities

Margin of error :

 lower limit 124.1 upper limit 152.9 margin of error 14.4

(c)

for 99% confidence level = (100-99)/100 = 0.01

/2 = 0.005

Z/2 = Z0.005 = 2.5758

99% confidence interval for the population mean annual number of reported larceny cases in such communities

Margin of error:

 lower limit 119.5 upper limit 157.5 margin of error 19

#### Earn Coins

Coins can be redeemed for fabulous gifts.