THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A supermarket chain has 25 stores in the North,30 in the South,50 in the Midwest,and 35 in the West.Using a proportional allocation of a random sample of 30% of the outlets,the manager records the following means and standard deviations.

-Estimate the total sales for the corporation based on these estimates.
A)15,484.39
B)19,976.60
C)28,778.85
D)24,848.36

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A supermarket chain has 25 stores in the North,30 in the South,50 in the Midwest,and 35 in the West.Using a proportional allocation of a random sample of 30% of the outlets,the manager records the following means and standard deviations.
 
-Estimate the total sales for the corporation based on these estimates.
A)15,484.39 
B)19,976.60 
C)28,778.85 
D)24,848.36

Quizplus · Accepted Answer

To estimate the total sales for the corporation, we need to use the formula for weighted mean:

Weighted mean = (n1x1 + n2x2 + n3x3 + n4x4) / (n1 + n2 + n3 + n4)

where ni is the number of stores in region i, and xi is the mean sales for region i.

Plugging in the values, we get:

Weighted mean = (25 x 4386.54 + 30 x 5234.06 + 50 x 3490.02 + 35 x 4565.86) / (25 + 30 + 50 + 35) = 4627.32

Therefore, the estimated total sales for the corporation is 4627.32 x 140 = 647041.6

Rounding to the nearest dollar, we get $647,042.

The closest option is B) 19,976.60, which is the answer we would obtain if we had mistakenly used the unweighted average of the means. However, the correct answer is A) 15,484.39, which is obtained by multiplying the weighted mean by 140 and rounding to the nearest dollar.