# The following data related to the number of children classified according to the type of feeding and nature of teeth. Type of feed Nature of teeth Normal Defective Breast 18 12 Bottle 2 13 Do the information provide sufficient evidence to conclude that type of feeding and nature of teeth are dependent? Use chi square test at 5% level of significance.

Problem to test

H0 : Type of feeding and nature of teeth are independent

H1 : Type of feeding and nature of teeth are dependent

 Type of feed Nature of Teeth Normal Defective Total Breast a=18 b=12 a+b=30 Bottle c=2 d=13 c+d=15 Total a+c=20 b+d=25 N=45

Test statistics

X2 = $$\frac{N(|ad – bc| – \frac{N}{2})^2}{(a+c)(b+d)(a+b)(c+d)}$$

= $$\frac{45(|18 x 13 – 12 x 2| – \frac{45}{2})^2}{20 x 25 x 30 x 25}$$

= 7.031

Critical Value

At α = 0.05 level of significance critical value is X2α(1) = 3.84

Decision

X2 = 7.031 > X20.01(1) = 3.84

Reject H0 at 0.05 level of significance

Conclusion

Type of feeding and nature of teeth are dependent