Answer Happy

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, x, 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 dx = 3.2 hours for the New York area and oy = 2.2 hours for the Miami, Florida area. We take a random sample of m = 23 New York commuters and n=39 Miami commuters. The mean numbers of hours commuting were X= 12.6 for the New York City area and y= 10.3 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 Mx - My. 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 x - Hy? d) What is the length of the confidence interval in part c) ? e) If we let n stay at 39 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.