The Postal Service Groups First-Class Mail As Letters And Ca

The Postal Service Groups First Class Mail As Letters Cards Flats O

The Postal Service Groups First Class Mail As Letters Cards Flats O

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

Total 79 148.20

S = 1

R-Sq = 10%

R-Sq(adj) = 6%

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 (H₀): There is no significant difference in the mean transit times among the different types of first-class mail (letters, cards, flats, parcels).

Alternate hypothesis (H₁): At least one type of first-class mail has a mean transit time that differs significantly from the others.

Decision Rule

Using the F-test from the analysis of variance, compare the calculated F-value to the critical F-value at the 0.01 significance level with numerator degrees of freedom (df₁=3) and denominator degrees of freedom (df₂=76). The critical F-value can be obtained from F-distribution tables or statistical software.

Alternatively, since the P-value associated with the F-statistic is 0.058, which is greater than the significance level of 0.01, we fail to reject the null hypothesis.

In conclusion, because the P-value exceeds 0.01, there is not enough statistical evidence at the 1% significance level to conclude that there are differences in mean transit times among the different types of first-class mail.

Full Paper

The analysis of variance (ANOVA) conducted on the postal service data aims to determine whether the type of first-class mail affects the mean transit times. The data presented includes the sum of squares (SS), mean squares (MS), F-statistic, and P-value for the factor (mail type), as well as the residual error.

The null hypothesis asserts that all four mail categories—letters, cards, flats, and parcels—share the same average transit time, implying no effect of mail type on transit duration. The alternative hypothesis posits that at least one category has a different mean transit time, indicating an effect of mail type.

The ANOVA results indicate a test statistic (F) of 2.60 with a corresponding P-value of 0.058. Given the significance level of 0.01, the P-value exceeds this threshold, suggesting that the evidence is insufficient to reject the null hypothesis. The conclusion is that, at the 1% significance level, there is no statistically significant difference in mean transit times among the different types of first-class mail.

It is important to note that while the P-value is close to 0.05, indicating marginal evidence against the null hypothesis, the strict criterion of 0.01 leads to accepting the null hypothesis. This conservative approach minimizes the chance of Type I errors but also reduces the likelihood of detecting subtle differences. Further research with larger samples or additional variables might provide more insight into transit time variations.

The relatively low R-squared value (10%) indicates that only a small proportion of the variability in transit times is explained by mail type, pointing to other factors influencing transit duration that are not captured in this analysis.

In summary, the statistical data suggests that, under the current conditions, mail type does not significantly impact the transit duration at the stringent 1% significance level. Postal services might consider other factors or additional data to optimize their delivery processes.

References

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