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 Somewhat Small 15 Medium 15 12 13 Small Lar 12 TOTALS In-Store On-Line Third-I 18 10 12 14 0 TOTALS: a. 3 points) Fill in the table of expected frequencies. Somewhat Somewhat Small Small Medium 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. 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

a)

as expected frequency =row total*column total/greand total

expected frequency table:

b)

applying chi square test of independence:

test statitic =29.813

c)

degree of freedom =(row-1)*(column-1)=(3-1)*(5-1)=8

d)

critcal value =20.090

e)

as test statitstic 29.813 is higher than crtiical value we reject null hypotheiss

f)

we have sufficient evidence to conclude that there is a relationship between an order's source and its size.

Expected Ei=?row*?column/?total small somewhat small medium somewhat large large Total in store 8.000 12.000 16.000 16.000 8.000 60 on-line 6.000 9.000 12.000 12.000 6.000 45 third party 6.000 9.000 12.000 12.000 6.000 45 Total 20 30 40 40 20 150

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