Answer Happy

Does the average(mean) commuting time in the New York City areadiffer from the mean commuting time in the Miami, Florida area? Themean number of hours, 𝜇x , of weekly commuting in the New York Cityarea will be compared to the mean number of hours, 𝜇y of weeklycommuting time in the Miami, Florida area. The true values of 𝜇xand 𝜇y are unknown. It is recognized that the true standarddeviations are 𝜎x = 3.2 hours for the New York area and 𝜎y = 2.2hours for the Miami, Florida area. We take a random sample of m =23 New York commuters and n=39 Miami commuters. The mean numbers ofhours commuting were x= 12.6 for the New York City area and y= 10.3for the Miami area. Assuming all measurements were independent fromone another and assuming that commuting times are normallydistributed we would like to estimate 𝜇x − 𝜇y . a) What is thestandard deviation of the distribution of y? b) What is thestandard deviation of the distribution of x - y ? c) Create a 95%confidence interval for 𝜇x − 𝜇y ? , d) What is the length of theconfidence interval in part c) ? e) If we let n stay at 39 but varym, what is the smallest m for which the length of the 95%confidence interval would be 2.0 or less?