A study by the highway authority wants to compare the distance traveled to the a
ID: 3153826 • Letter: A
Question
A study by the highway authority wants to compare the distance traveled to the airport by employees in Philadelphia and those in New York City. A sample of 35 Philadelphia employees shows they travel a mean of 370 miles per month to the airport. A sample of 40 NYC employees shows they drive a mean of 380 miles per month to the airport. The population standard deviation for the Philadelphia employees is 30 miles and the population standard deviation for the NYC employees is 26 miles. Is there a difference in the mean number of miles traveled per month to the airport between the Philadelphia employees and the NYC employees?
Conduct the following test of hypothesis using the .05 significance level
What is your decision regarding Ho based on the decision rule (rejection region) What is the p-value What is your decision based on the p-value What can you conclude?
ANY IDEA?
Explanation / Answer
Set Up Hypothesis
Null,no difference in the mean number of miles traveled per month to the
airport between the Philadelphia employees and the NYC employees Ho: u1 = u2
Alternate Hypothesis , there Is Significance between them H1: u1 != u2
Test Statistic
X(Mean)=370
Standard Deviation(s.d1)=30
Number(n1)=35
Y(Mean)=380
Standard Deviation(s.d2)=26
Number(n2)=40
we use Test Statistic (Z) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=370-380/Sqrt((900/35)+(676/40))
Zo =-1.53
| Zo | =1.53
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo | =1.532 & | Z | =1.96
Make Decision
Hence Value of | Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -1.53 ) = 0.12555
Hence Value of P0.05 < 0.12555,Here We Do not Reject Ho
no difference in the mean number of miles traveled per month to the airport between the Philadelphia employees and the NYC employees
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.