Answer:
Given data
A certain manufacturing firm produces a product that is packaged under 2 brand
The sample for brand 1 was taken from a list of 120 customers for who the total sales in the same quater of last year was 24 units
the brand 2 sample come from 180customers with a total quarterly sales last year of 21200 units
x i | y i | (y - ![]() |
204 | 210 | 16.33332 |
143 | 140 | 99.22431 |
82 | 75 | 121.7992 |
256 | 280 | 129.9364 |
275 | 300 | 131.4171 |
198 | 190 | 314.9246 |
total = 1158 |
total = 1215 |
total = 813.6349 |
Now let T s = total sales
= 24,500
=
=
= 202.5
=
=
= 193
Let ratio etimator
=
=
= 1.049223
This total ratio estimate
Tx
=
Tx
= 1.049223 * 24500
= 25705.96
Let
=
=
= 162.727
Variance
=
=
=
= 433581200.7
Let SD
= 20822.612
Brand 2
xi | yi | (Y - ![]() |
137 | 150 | 21.122392 |
189 | 200 | 0.352792 |
119 | 125 | 1.6897447 |
63 | 60 | 47.12348 |
103 | 110 | 0.464574 |
107 | 100 | 183.9761 |
159 | 180 | 126.4804 |
63 | 75 | 66.18385 |
87 | 90 | 5.461118 |
Total = 1027 | 1090 | 452.8544 |
Let Tr = Total sales = 21200
= 121.111
= 114.111
Let estimator
= 22500.49
where
= 50.32
Let Var
= 191938.53
where
= 438.11
By solving both Brand (1) & Brand (2)
SD Brand 2 < SD Brand 1
Therefore Brand 2 data is the best data.
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Sum
of
Mean
Source
Freedom
Squares
Squares
F
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Error
18
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Total
20
180
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