Question

The processing time for the shipping of packages for a company, during the holidays, were recorded for 48 different orders. The mean of the 48 orders is 10.5 days and the standard deviation is 3.08 days. Raw data is given below. Use a 0.05 significance level to test the claim that the mean package processing time is less than 12.0 days. Is the company justified in stating that package processing is completed in under 12 days?

1) Write Ho (null) and H1 (alternative) and indicate which is being tested

2) Perform the statistical test and state your findings; Write answer as a statement

Days
4.4
8.8
8.2
11.5
11
15.3
10.3
10.9
4.8
13.6
8.1
4.1
12.5
9.9
11.3
13.1
13.6
7.6
10.3
11.7
8.9
4
9.5
8.1
16.3
13.7
12.4
8.6
13.8
7.1
6.9
11.3
9.9
11.8
12.2
11.4
6.2
10
12.7
11.3
13.2
12
9
10
13.3
16.8
14.9
7.7

Answer 1

To Test :-

H0 :-  

H1 :-

Test   Statistic :-                               
               
                   
t = -3.3741              

               
Test   Criteria :-                                
                          
               
           

Conclusion :- Accept Alternative Hypothesis

                        

There is sufficient evidence to support the claim that the mean package processing time is less than 12.0 days at 5% level of significance.