Question

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 230 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample the mean commute time is 28.6 minutes with a standard deviation of 19.3 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the p-value for this hypothesis test?

Answer 1

Ho :   µ =   30                  
Ha :   µ <   30       (Left tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s =    19.3000                  
Sample Size ,   n =    230                  
Sample Mean,    x̅ =   28.6000                  
                          
degree of freedom=   DF=n-1=   229                  
                          
Standard Error , SE = s/√n =   19.3   / √    230   =   1.2726      
t-test statistic= (x̅ - µ )/SE = (   28.600   -   30   ) /    1.273 =   -1.100
                          
  
p-Value   =   0.1362   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis                       
Conclusion: There is not enough evidence to conclude that the mean commute time in the U.S. is less than half an hour at the 5% level of significance