You are employed as a statistician for a company that makes household products,
ID: 3251223 • Letter: Y
Question
You are employed as a statistician for a company that makes household products, which are sold by part-time salespersons who work during their spare time. The company has four salespersons employed in a small town. Let us denote these salespersons by A, B, C, and D.
The sales records (in dollars) for the past 6 weeks for these four salespersons are shown in the table below.
Week
A
B
C
D
1
1774
2205
1330
1402
2
1808
1507
1295
1665
3
1890
2352
1502
1530
4
1932
1939
1104
1826
5
1855
2052
1189
1703
6
1726
1630
1441
1498
Your supervisor has asked you to prepare a brief report comparing the sales volumes and the consistency of sales of these four salespersons.
Use the mean sales for each salesperson to compare the sales volumes.
Choose an appropriate statistical measure to compare the consistency of sales.
Make the calculations and write a 700-word report comparing the sales volumes and the consistency of sales of these four salespersons.
Week
A
B
C
D
1
1774
2205
1330
1402
2
1808
1507
1295
1665
3
1890
2352
1502
1530
4
1932
1939
1104
1826
5
1855
2052
1189
1703
6
1726
1630
1441
1498
Explanation / Answer
A=x1=10985/6=1830.83
B=x2=11685/6=1947.5
C=x3=7861/6=1310.17
D=x4=9624/6=1604
X=1830.83+1947.5+1310.17+1604/4=1673.125
X=273.2, n=24, c=4
SSA=6(1830.83-1673.125)2+……6(1604-1673.125)2=1420023.45833333
SSW= (1774-1830.83)2+ ……(1498-1604)2=796875.166666667
MSA=1420023.45833333/(4-1) =473341.152777778
MSW=796875.166666667/(24-4) =39843.7583333333
FSTAT=473341.152777778/39843.7583333333=11.8799323301231
FSTAT is greater than FCRIT and hence reject the null hypothesis. One of the means is different and hence there is a difference in the average sales by salespersons.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 6 10985 1830.833333 5812.166667 B 6 11685 1947.5 107153.1 C 6 7861 1310.166667 22345.36667 D 6 9624 1604 24064.4 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1420023.458 3 473341.1528 11.87993233 0.000109305 3.098391212 Within Groups 796875.1667 20 39843.75833 Total 2216898.625 23A=x1=10985/6=1830.83
B=x2=11685/6=1947.5
C=x3=7861/6=1310.17
D=x4=9624/6=1604
X=1830.83+1947.5+1310.17+1604/4=1673.125
X=273.2, n=24, c=4
SSA=6(1830.83-1673.125)2+……6(1604-1673.125)2=1420023.45833333
SSW= (1774-1830.83)2+ ……(1498-1604)2=796875.166666667
MSA=1420023.45833333/(4-1) =473341.152777778
MSW=796875.166666667/(24-4) =39843.7583333333
FSTAT=473341.152777778/39843.7583333333=11.8799323301231
FSTAT is greater than FCRIT and hence reject the null hypothesis. One of the means is different and hence there is a difference in the average sales by salespersons.
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