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.

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Login Now**Problem to test**

H_{0} : Type of feeding and nature of teeth are independent

H_{1} : 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**

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

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

= 7.031

**Critical Value**

At α = 0.05 level of significance critical value is X^{2}_{α(1)} = 3.84

**Decision**

X^{2} = 7.031 > X^{2}_{0.01(1)} = 3.84

Reject H_{0} at 0.05 level of significance

**Conclusion**

Type of feeding and nature of teeth are dependent

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## Discussion