Does the average(mean) commuting time in the New York City area differ from the mean commuting time in the Miami, Florida area? The mea number of hours, μx, of weekly commuting in the New York City area will be compared to the mean number of hours, y of weekly commuting time in the Miami, Florida area. The true values of μx and μy are unknown. It is recognized that the true standard deviations are x = 1.8 hours for the New York area and oy = 2.8 hours for the Miami, Florida area. We take a random sample of m = 27 New York commuters and n=34 Miami commuters. The mean numbers of hours commuting were x= 13.6 for the New York City area and y= 11.3 for the Miami area. Assuming all measurements were independent from one another and assuming that commuting times are normally distributed we would like to estimate x-μy. a) What is the standard deviation of the distribution of y? b) What is the standard deviation of the distribution of x-y? c) Create a 95% confidence interval for Mx - Hy? ([ d) What is the length of the confidence interval in part c) ? e) If we let n stay at 34 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 2.0 or less? f) Copy your R script for the above into the text box here.
Does the average(mean) commuting time in the New York City area differ from the mean commuting time in the Miami, Florida area? The mea number of hours, μx, of weekly commuting in the New York City area will be compared to the mean number of hours, y of weekly commuting time in the Miami, Florida area. The true values of μx and μy are unknown. It is recognized that the true standard deviations are x = 1.8 hours for the New York area and oy = 2.8 hours for the Miami, Florida area. We take a random sample of m = 27 New York commuters and n=34 Miami commuters. The mean numbers of hours commuting were x= 13.6 for the New York City area and y= 11.3 for the Miami area. Assuming all measurements were independent from one another and assuming that commuting times are normally distributed we would like to estimate x-μy. a) What is the standard deviation of the distribution of y? b) What is the standard deviation of the distribution of x-y? c) Create a 95% confidence interval for Mx - Hy? ([ d) What is the length of the confidence interval in part c) ? e) If we let n stay at 34 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 2.0 or less? f) Copy your R script for the above into the text box here.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Does the average(mean) commuting time in the New York City area differ from the mean commuting time in the Miami, Florida area? The mean
number of hours, μx, of weekly commuting in the New York City area will be compared to the mean number of hours, y of weekly
commuting time in the Miami, Florida area. The true values of μx and μy are unknown. It is recognized that the true standard deviations are
x = 1.8 hours for the New York area and oy = 2.8 hours for the Miami, Florida area. We take a random sample of m = 27 New York
commuters and n=34 Miami commuters. The mean numbers of hours commuting were x= 13.6 for the New York City area and y= 11.3 for the
Miami area. Assuming all measurements were independent from one another and assuming that commuting times are normally distributed we
would like to estimate x-μy.
a) What is the standard deviation of the distribution of y?
b) What is the standard deviation of the distribution of x-y?
c) Create a 95% confidence interval for Mx - Hy? ([
d) What is the length of the confidence interval in part c) ?
e) If we let n stay at 34 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 2.0 or less?
f) Copy your R script for the above into the text box here.
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