Question

In: Statistics and Probability

A large consumer electronics retailer is planning to expand its e-commerce operations. To this end, the...

A large consumer electronics retailer is planning to expand its e-commerce operations. To this end, the management is considering establishing a strategic partnership with courier company XYZ for the delivery of customers’ orders.

Estimate the extend of the difference in delivery times between ABC and XYZ at 95% confidence level.

Company ABC Company XYZ
18,42280727 18,11722091
23,25971383 18,03236506
24,47267508 11,70181582
16,43125944 28,6349246
24,28843419 20,01970193
28,94755272 21,43805892
23,99634997 25,77991841
21,24041049 17,61727736
13,03788468 23,17141939
22,48407401 19,44828346
11,75437848 16,47678806
25,32910531 27,07743766
28,29293481 22,60188244
18,07510972 21,75405717
18,52644874 17,69497663
27,387692 17,85126192
31,33021511 26,10624511
17,54311671 21,061494
19,60308128 20,38612598
24,13955445 23,3838603
22,91021548 27,90996637
24,93664016 15,98477416
17,39909368 15,16035132
23,66404789 21,78663413
26,33621608 25,21042693
34,52750735 25,72431418
28,47319212 22,36474307
20,53729378 21,05484901
21,29081923 20,54825477
14,71201432 16,49442088
24,47566959 15,64039399
14,28379238 18,38440203
12,40888724 23,25464953
18,93436393 18,26911221
29,47781996 18,64149345
22,68654117 25,70740895
22,51631105 20,85214458
24,03909167 23,93770199
31,76300726
17,96011776
28,38274287
17,65424787
27,28002602
22,83645773
23,3062072
15,58564764
25,03221213
20,24033921
26,41886186
18,33414518

Write the relevant formulas in each case and show your calculations. Use appropriate tools from the Data Analysis Toolpak to verify your conclusions

Solutions

Expert Solution

Degree of freedom, DF=   n1+n2-2 =    86              
t-critical value =    t α/2 =    1.9879   (excel formula =t.inv(α/2,df)          
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    650439982.9385              
                      
std error , SE =    Sp*√(1/n1+1/n2) =    139981861.7642              
margin of error, E = t*SE =    1.9879   *   139981861.7642   =   278274731.2541  
                      
difference of means =    x̅1-x̅2 =    2137753853.0800   -   1914772029.500   =   222981823.5800
confidence interval is                       
Interval Lower Limit=   (x̅1-x̅2) - E =    222981823.5800   -   278274731.2541   =   -55292907.6741
Interval Upper Limit=   (x̅1-x̅2) + E =    222981823.5800   +   278274731.2541   =   501256554.8341

Please revert in case of any doubt.

Please upvote. Thanks in advance

orchestra answered 1 year ago
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