## 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 |
---|---|---|---|---|

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

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

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

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

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

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

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

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

**b**. Do these data provide sufficient proof to show differences in the mean weight per brochure among the five cartons?

Solution

VerifiedGiven:

$\begin{align*} \alpha&=\text{Significance level}=0.05 &\textcolor{#4559AC}{(\text{Assumption})} \\ k&=\text{Number of groups}=4 \end{align*}$

We need to execute a one-way ANOVA hypothesis test and a multiple comparison test.

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