Homework SourseA Conduct a two sample Ttest to see if the average number of
A.) Conduct a two sample T-test to see if the average number of units sold is the same or different for the South and North regions.
B.) Is there a difference between the two regions for units sold? How do you know?
(Please show steps for T-test)
| Store and Regional Sales Database | ||
| Sales Region | Units Sold | Week Ending |
| South | 28 | October |
| South | 30 | November |
| South | 9 | December |
| South | 30 | October |
| South | 35 | November |
| South | 39 | December |
| South | 28 | October |
| South | 3 | November |
| South | 38 | December |
| South | 25 | October |
| South | 27 | November |
| South | 33 | December |
| South | 8 | October |
| South | 8 | November |
| South | 10 | December |
| South | 8 | October |
| South | 8 | November |
| South | 8 | December |
| South | 9 | October |
| South | 9 | November |
| South | 8 | December |
| South | 18 | October |
| South | 18 | November |
| South | 20 | December |
| South | 38 | October |
| South | 30 | November |
| South | 3 | December |
| South | 30 | October |
| South | 32 | November |
| South | 33 | December |
| South | 25 | October |
| South | 5 | November |
| South | 26 | December |
| South | 28 | October |
| South | 27 | November |
| South | 29 | December |
| North | 18 | October |
| North | 20 | November |
| North | 4 | December |
| North | 12 | October |
| North | 24 | November |
| North | 36 | December |
| North | 29 | October |
| North | 11 | November |
| North | 38 | December |
| North | 21 | October |
| North | 24 | November |
| North | 30 | December |
| North | 27 | October |
| North | 25 | November |
| North | 23 | December |
| North | 80 | October |
| North | 82 | November |
| North | 75 | December |
| North | 65 | October |
| North | 24 | November |
| North | 55 | December |
| North | 55 | October |
| North | 57 | November |
| North | 47 | December |
Solution
Set Up Hypothesis
Null , There Is No-Significance between them Ho: u1 = u2
Alternate , There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=21.194
Standard Deviation(s.d1)=11.538 ; Number(n1)=36
Y(Mean)=36.75
Standard Deviation(s.d2)=22.464; Number(n2)=24
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =21.194-36.75/Sqrt((133.12544/36)+(504.6313/24))
to =-3.129
| to | =3.129
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 23 d.f is 2.069
We got |to| = 3.1285 & | t | = 2.069
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -3.1285 ) = 0.005
Hence Value of P0.05 > 0.005,Here we Reject Ho
[ANSWER]
We have enough evidence that average number of units sold is different for the
South and North regions
