2. (10 points) A retailer divided its orders by size into five classes: Small, S

Question

2. (10 points) A retailer divided its orders by size into five classes: Small, Somewhat small, Medium, Somewhat large, Large. It wants to see whether the size of an order depends on the source of the order: In-store, On-line, Third-party. A sample of 150 orders resulted in the contingency table below Somewhat Small 15 Somewhat Large 18 10 12 Small Medium 15 12 13 Large TOTALS In-Store On-Line Third-Party 12 14 TOTALS (3 points) Fill in the table of expected frequencies a. Somewhat Small Somewhat Large Small Medium Large TOTALS In-Store On-Line Third-Party TOTALS b.(3 points) Calculate the value of the test statistic c.(1 point) How many degrees of freedom does this test of independence have? d. (1 point) What is the critical value of the test statistic? Use = 0.01 e. (1 point) Can the retailer reject the null hypothesis? f.(1 point) Is there sufficient evidence to say that there is a relationship between an order's source and its size?

Explanation / Answer

Ans:

a,b)Expected count=row sum*column sum/overall sum

test statistic=29.813

c)df=(r-1)*(c-1)=(3-1)*(5-1)=2*4=8

d)critical chi square score=CHIINV(0.01,8)=20.090

e)As,calculated chi square score=29.813>20.090,so we reject null hypothesis.

f)There is sufficient evidence to conclude that there is a relationship between an order's source and its size.

Observed(O) small somewhat small medium somewhat large large Total In-store 0 15 15 18 12 60 On-Line 6 9 12 10 8 45 Third party 14 6 13 12 0 45 Total 20 30 40 40 20 150 Expected(E) small somewhat small medium somewhat large large Total In-store 8 12 16 16 8 60 On-Line 6 9 12 12 6 45 Third party 6 9 12 12 6 45 Total 20 30 40 40 20 150 Chi square=(O-E)^2/E small somewhat small medium somewhat large large In-store 8.000 0.750 0.063 0.250 2.000 On-Line 0.000 0.000 0.000 0.333 0.667 Third party 10.667 1.000 0.083 0.000 6.000 Total chi square score=29.813

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