## Answers

1)

a)

1st group | 2nd group | |

x= | 83 | 74 |

n = | 500 | 500 |

p̂=x/n= | 0.1660 | 0.1480 |

estimated prop. diff =p̂_{1}-p̂_{2} = | 0.0180 | |

pooled prop p̂ =(x_{1}+x_{2})/(n_{1}+n_{2})= | 0.1570 | |

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) = | 0.0230 | |

test stat z=(p̂1-p̂2)/Se = | 0.78 | |

P value = | 0.4354 | (from excel:2*normsdist(-0.78) |

b)

first sample proportion p1 = | 0.2 | ||

second sample proportion p2= | 0.25 | ||

0.05 level critical Z= | 1.96 | ||

0.1 level critical Zβ= | 1.28 | ||

n=((z_{α}(√(p1+p2)*(q_{1}+q_{2})/2)+z_{β}(√p_{2}q_{2}+p_{2}q_{2}))/(p_{1}-p_{2}))^{2}= | 1465 |

2)Applying ANOVA:

Source of Variation | SS | df | MS | F | P-value |

Between Groups | 22781.2546 | 3 | 7593.7515 | 4.4882 | 0.0145 |

Within Groups | 33838.9750 | 20 | 1691.9488 | ||

Total | 56620.2296 | 23 |

f =4.49

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