Question

In: Statistics and Probability

Study Guide #2 Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of...

Study Guide #2

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that ? is known to be 42.9 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    


(d) Compare the margins of error for parts (a) through (c).

As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error increases.

As the confidence level increases, the margin of error remains the same.  

As the confidence level increases, the margin of error decreases.


(e) Compare the lengths of the confidence intervals for parts (a) through (c).

As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval increases in length.

As the confidence level increases, the confidence interval decreases in length.    

As the confidence level increases, the confidence interval remains the same length.

Solutions

Expert Solution

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that ? is known to be 44.5 cases per year
given
x bar = 138.5
? (std)= 42.9
n=33
(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?
     z score = 1.645
ME = 1.645*42.9/sqrt(33) = 12.28
lower limit = 138.5-12.28 = 126.22
upper limit = 138.5+12.28 = 150.78

(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?
     z score = 1.96
ME = 1.96 * 42.9/sqrt(33) = 14.64
lower limit = 138.5-14.64 = 123.86
upper limit = 138.5+14.64 = 153.14

(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?
     z score = 2.58
ME = 2.58 * 42.9/sqrt(33) = 19.27
lower limit = 138.5-19.27 = 119.23
upper limit = 138.5+19.27 = 157.77

(d) Compare the margins of error for parts (a) through (c).

As the confidence level increases, the margin of error increases

(e) Compare the lengths of the confidence intervals for parts (a) through (c)

As the confidence level increases, the confidence interval increases in length.


Related Solutions

Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5...
Thirty-three 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 43.1 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...
Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5...
Thirty-three 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 43.9 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...
Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5...
Thirty-three 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 43.7 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...
Thirty-three small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5...
Thirty-three 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 43.7 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...
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 40.9 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...
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 41.5 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...
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 41.9 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...
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 40.3cases 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...
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 44.9 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...
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 45.1 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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT