Question

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

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.
Question 1
The management of the retailer is prepared to proceed with the partnership only if XYZ can deliver orders faster than company ABC that is currently used by the retailer. The e-commerce department of the retailer has collected data from 50 random orders delivered by ABC in the last two months and 38 similar random orders delivered by XYZ in the same period. The data is included in the table below and refer to the time (in hours) between the placement of each order and the delivery to the customer. Use an appropriate statistical test to advise the management of the retailer whether or not they should partner with XYZ.

Answer 1

Two-Sample T-Test and CI: Company XYZ, Company ABC

Method

μ₁: mean of Company XYZ

µ₂: mean of Company ABC

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Company XYZ	38	1914772030	634053480	102857057
Company ABC	50	2137753853	662544963	93698007

Estimation for Difference

Difference	95% Upper Bound for Difference
-222981824	8524712

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ < 0

Null hypothesis H₀: μ₁ - µ₂ = 0

Alternative hypothesis H₁: μ₁ - µ₂ < 0 ( XYZ company is delivering faster than ABC company)

test statistic t =  

df =

T-Value	DF	P-Value
-1.60	81	0.056

Since p-value is more than alpha 0.05 we fail to reject H0 and there is no sufficient evidence to conclude that XYZ company is delivering faster than ABC company. Hence the management of the retailer should not partner with XYZ.