Question

A manufacturing company is purchasing metal pipes of standard length from two different suppliers, ABC and XYZ. In the past two months there are increasing complaints by the Production Manager that delivery times by ABC present higher variability in comparison to the delivery times by XYZ. The Production Manager is worried that this variability will make it harder to efficiently schedule the production process. If the variance of XYZ remains unchanged, what should be the variance of ABC in order to reject the null hypothesis at 5% significance level?

Delivery Times(in Hours) by Suppliers ABC and XYZ on
Selected Orders |
||||

Order | Supplier ABC | Order | Supplier XYZ | |

1 | 35 | 1 | 19 | |

2 | 26 | 2 | 23 | |

3 | 26 | 3 | 22 | |

4 | 30 | 4 | 21 | |

5 | 25 | 5 | 26 | |

6 | 20 | 6 | 24 | |

7 | 24 | 7 | 23 | |

8 | 25 | 8 | 17 | |

9 | 19 | 9 | 24 | |

10 | 27 | 10 | 21 | |

11 | 29 | 11 | 28 | |

12 | 25 | 12 | 30 | |

13 | 12 | 13 | 20 | |

14 | 20 | 14 | 34 | |

15 | 22 | 15 | 23 | |

16 | 17 | 16 | 26 | |

17 | 21 | 17 | 28 | |

18 | 16 | 18 | 28 | |

19 | 32 | 19 | 26 | |

20 | 23 | 20 | 30 | |

21 | 29 | 21 | 36 | |

22 | 22 | 22 | 22 | |

23 | 12 | 23 | 20 | |

24 | 28 | 24 | 22 | |

25 | 24 | 25 | 21 | |

26 | 27 | |||

27 | 18 |

Answer #1

σ₁: standard deviation of Supplier ABC |

σ₂: standard deviation of Supplier XYZ |

Ratio: σ₁/σ₂ |

F method was used. This method is accurate for normal data only. |

Descriptive Statistics

Variable | N | StDev | Variance | 95% Lower Bound for σ² |

Supplier ABC | 27 | 5.618 | 31.567 | 21.107 |

Supplier XYZ | 25 | 4.638 | 21.507 | 14.174 |

Ratio of Variances

Estimated Ratio |
95% Lower Bound for Ratio using F |

1.46778 | 0.746 |

The hypothesis being tested is:

Null hypothesis | H₀: σ₁² / σ₂² = 1 |

Alternative hypothesis | H₁: σ₁² / σ₂² > 1 |

Significance level | α = 0.05 |

Method | Test Statistic |
DF1 | DF2 | P-Value |

F | 1.47 | 26 | 24 | 0.174 |

The p-value is 0.174.

Since the p-value (0.174) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a statistically significant difference.

A manufacturing company is purchasing metal pipes of standard
length from two different suppliers, ABC and XYZ. In the past two
months there are increasing complaints by the Production Manager
that delivery times by ABC present higher variability in comparison
to the delivery times by XYZ. The Production Manager is worried
that this variability will make it harder to efficiently schedule
the production process.
Does the sample data indicate a statistically significant
difference at the 5% level? Justify your answer....

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