Question

Two computer stores recorded the number of computers sold in a week along with the sizes of their hard drives. At , test the claim that the distribution of hard drives and the store where the computers were bought are not related. Number of computers 20 GB drive 40 GB drive 80 GB drive 160 GB drive Store 1 14 10 13 11 Store 2 117 40 26 10

Answer 1

null hypothesis: Ho:distribution of hard drives and the store where the computers were bought are not related.

alternate hypothesis:Ha:distribution of hard drives and the store where the computers were bought are related

degree of freedom(df) =(rows-1)*(columns-1)=

3

for 3 df and 0.05 level of signifcance critical region       χ2=

7.815

Applying chi square test of independence:

Observed	Oi	20 GB	40 GB	80 GB	160 GB
	store 1	14	10	13	11
	store 2	117	40	26	10
	Total	131	50	39	21
Expected	Ei=Σrow*Σcolumn/Σtotal	20 GB	40 GB	80 GB	160 GB
	store 1	26.09	9.96	7.77	4.18
	store 2	104.91	40.04	31.23	16.82
	Total	131	50	39	21
chi square    χ2	=(Oi-Ei)2/Ei	20 GB	40 GB	80 GB	160 GB
	store 1	5.6034	0.0002	3.5246	11.1121
	store 2	1.3936	0.0000	0.8766	2.7636
	Total	6.997	0.000	4.401	13.876

test statistic χ²=13.876

Decision:as test statistic is in rejection region we reject null hypothesis

Conclusion: we have sufficient evidence to conclude that distribution of hard drives and the store where the computers were bought are related