Question

You are considering a new delivery system and wish to test whether delivery times are significantly different on average than your current system. It is well established that the mean delivery time of the current system is 2.38 days. A test of the new system shows that with 48 observations the average delivery time is 1.91 days with a standard deviation of 0.43 day.

A) perform a two-sided test at the 1% significance level and describe the result.

B) State the p-value as either p >0.05, p<0.05, p<0.01, or p<0.001.

C) Summarize the results in a brief memo to management.

Answer 1

a)

Ho :   µ =   2.38                  
Ha :   µ ╪   2.38       (Two tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s =    0                  
Sample Size ,   n =    48                  
Sample Mean,    x̅ =   2                  
                          
degree of freedom=   DF=n-1=   47                  
                          
Standard Error , SE = s/√n =   0.4300   / √    48   =   0.0621      
t-test statistic= (x̅ - µ )/SE = (   1.910   -   2.38   ) /    0.0621   =   -7.57
                             
                          
p-Value   =   0.0000   [Excel formula =t.dist(t-stat,df) ]              

b)

p<0.001.

c)

Decision:   p-value<α, Reject null hypothesis

It can be conculded that delivery times are significantly different on average than your current system

THANKS

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