## Related questions with answers

A direct-mail company assembles and stores paper products (envelopes, letters, brochures, order cards, etc.) for its customers. The company estimates the total number of pieces received in a shipment by calculating the weight per piece and then weighing the entire shipment. The company is unsure whether the sample of pieces used to estimate the mean weight per piece should be drawn from a single carton or whether it is worth the extra time required to pull a few pieces from several cartons. To aid management in making a decision, eight brochures were removed from each of the five cartons of a typical shipment and weighed. The weights (in pounds) are displayed in the table.

Carton 1 | Carton 2 | Carton 3 | Carton 4 | Carton 5 |
---|---|---|---|---|

$.01851$ | $.01872$ | $.01869$ | $.01899$ | $.01882$ |

$.01829$ | $.01861$ | $.01853$ | $.01917$ | $.01895$ |

$.01844$ | $.01876$ | $.01876$ | $.01852$ | $.01884$ |

$.01859$ | $.01886$ | $.01880$ | $.01904$ | $.01835$ |

$.01854$ | $.01896$ | $.01880$ | $.01923$ | $.01889$ |

$.01853$ | $.01879$ | $.01882$ | $.01905$ | $.01876$ |

$.01844$ | $.01879$ | $.01862$ | $.01924$ | $.01891$ |

$.01833$ | $.01879$ | $.01860$ | $.01893$ | $.01879$ |

**c**. What deductions must be satisfied for the test of the part $\mathbf{b}$ to be valid?

Solution

VerifiedWe need to determine the required assumptions for executing a one-way ANOVA test.

Conditions for executing a one-way ANOVA test:

- Every treatment population has an approximately normal distribution.
- All treatment populations have the same variance.

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