Question

The table lists the sugar content of two types of apples from three different orchards. At , test the claim that the sugar content of the apples and the orchard where they were grown are not related. Sugar Content Orchard 1 Orchard 2 Orchard 3 Apple Type 1 4 2 6 Apple Type 2 28 10 14

Answer 1

null hypothesis:Ho:  sugar content of apples and the orchard where they are grown are not related

alternate hypothesis: Ha: sugar content of apples and the orchard where they are grown are related

adding orchard and orchard 3 column into 1 to make expected frequency in each cell more then 5.

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

1

for 1 df and 0.05 level of signifcance critical region       χ2=

3.841

Observed	Oi	orchard 1	orchard 2-3	Total
	type 1	4	8	12
	type 2	28	24	52
	Total	32	32	64
Expected	Ei=Σrow*Σcolumn/Σtotal	orchard 1	orchard 2-3	Total
	type 1	6.00	6.00	12
	type 2	26.00	26.00	52
	Total	32	32	64
chi square    χ2	=(Oi-Ei)2/Ei	orchard 1	orchard 2-3	Total
	type 1	0.6667	0.6667	1.333
	type 2	0.1538	0.1538	0.308
	Total	0.821	0.821	1.641

Decision: as test statistic is not in rejection region we fail to reject null hypothesis  

Conclusion:we do not have sufficient evidence to conclude that t sugar content of apples and the orchard where they are grown are related