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 | E_{i}=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
χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
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 χ^{2}=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

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