Question

A company needs to budget for fuel, they have to consider the weight of the shipment.

Average weight= 20,160 pounds

The CEO wonders if preferences have changed and you have to adjust the budget for fuel. Based on 14 shipments, the average weight has been 20,901 pounds with a sample standard deviation of 800 pounds. What should you conclude at the 99% confidence level?

Show your work on the calculated score (Commands from Excel)

Indicate what your calculated score is

Indicate and justify what your critical score is and determine if this sample average is statistically significant from the mean

Answer 1

Ho :   µ =   20160                  
Ha :   µ ╪   20160       (Two tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s =    800.0000                  
Sample Size ,   n =    14                  
Sample Mean,    x̅ =   20901.0000                  
                          
degree of freedom=   DF=n-1=   13                  
                          
Standard Error , SE = s/√n =   800.0000   / √    14   =   213.8090      
t-test statistic= (x̅ - µ )/SE = (   20901.000   -   20160   ) /    213.8090   =   3.466
                          
critical t value, t* =    ±   3.0123   [Excel formula =t.inv(α/2 , 13) ]              

since, test stat = 3.466 > critical value = 3.012 , reject Ho

Conclusion: There is enough evidence to conclude that sample average is statistically significant from the mean