# Maths – the postal service groups first-class mail as letters

The postal service groups first-class mail as letters, cards, flats, or parcels. Over a period of three weeks, one item of each kind was sent from a particular postal administrative center. The total time in transit was recorded. A statistical software package was then used to perform the analysis. The results follow.

Source DF SS MS F P
Factor 3 13.81 4.60 2.60 .058
Error 76 134.39 1.77

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Total 79 148.20

S = 1 R-Sq = 10% R-Sq(adj) = 6%
S = 1 R-Sq = 10% R-Sq(adj) = 6%

Level N Mean StDev
Letters 20 1.492 1.017
Cards 20 1.645 1.481
Flats 20 2.499 1.647
Parcels 20 2.443 .953

Use the 0.01 significance level to test if this evidence suggests a difference in the means for the different types of first-class mail.

Requirement (1a):
Identify the null hypothesis and the alternate hypothesis.

Null hypothesis:
Ho: μ1 = μ2 = μ3 = μ4
Ho: μ1 ≠ μ2 ≠ μ3 ≠ μ4
Alternate hypothesis:
H1: At least one mean is different.
H1: All means are equal
What is the decision rule? Use the 0.01 significance level. (Hint: using Megastat function.) (Round your answer to 4 decimal places.)

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