A.) Conduct a two sample T-test to see if the average number of units sold is th

Question

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

Explanation / Answer

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

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