Four salesmen in XYZ Company are competing for the title Salesman of the year. E

Question

Four salesmen in XYZ Company are competing for the title Salesman of the year. Each has the task of selling milk in three different types of location. Their resulting sales, in K' 000, were as follows: Area Salesmen 52.8 60.1 62.0 49.4 48.1 56.4 58.6 61.0 63.3 42.9 50.3 61.2 (a) Write down a model for the above design. Explain each term in the model in the context of the given information. (b) Consider the observation on the salesman B and location 2 (x,2 48.1) 2I Pag e Estimate ii. Estimate and interpret B ii. Estimate and interpret r iv. Estimate e (c) What is the blocking variable and what is the treatment? (d) What is the purpose of the blocks in this experiment? (e) Prepare a two-way analysis of variance table (f) Test at 5% level of significance the null hypothesis that the population mean sales are identical for all the four salesmen. (g) Test at 5% level of significance the null hypothesis that the population mean sales are the same for all three locations (h) Which salesman won? Did he do significantly better than his nearest rival?

Explanation / Answer

a. The model is Xij = M+ ti+bj + eij   i=1,2,3,4 j= 1,2,3

Where Xij= observed sales of i th salesman in the jth Area

M= over all mean sales

ti= Effect of ith salesman

bj = Effect of jth Area

eij= Error effect

b) When we consider X22= 48.1

M= overall mean = 55.508

ti= Effect of i th salesman= ith salesman mean - M= 51.3 - 55.508= - 4.208

  

bj = Effect of jth area = jth area - M= 54.875 - 55.508= - 0.633

eij= Error effect= Xij- M+ti+bj =- 2.567

c' Blocking variable is Area and treatment is salesman

d.Block means an homogeneous area

the purpose of blocking is to devide the whole into different areas and to test whether sales between the areas is significantly different or not

e. Two way ANOVA table

f)we observe that Fcal value of areas = 7.9859 is greater than Ftab value at 5% = 5.14

so we conclude that Aareas found significantly different with respect to sales

g)simillarly Fcal value of salesman = 5.8832 is also greater than F tab value at 5% =4.76

so we conclude that salesmans are also significantly different withrespect to sales

h) least significant difference between the salesmans = 6.9805

we observe that when we compare salesman C with B and D the mean difference between them is greater than L.S.D

hence salesman C is more better than salesman B and D

but the mean difference between salesman A and C is lessthan L.S.D

hence A and c are significantly not different but A and D are not significantly different

Hence C is most significant salesman among all the salesmen

  

Source of variation D.F S.S M.S.S variance ratio Ftab value at 5% Area 2 194.4875 97.24375 7.9859 5.14 salesman 3 214.92 71.64 5.8832 4.76 Error 6 73.0615 12.1769 Total 11 482.469

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