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# Design and Analysis of an Experiment Question

From time to time, one branch office of a company must make shipments to a certain branch office in another state. There are three package delivery services between the two cities where the branch offices are located. Since the price structures for the three delivery services are quite similar, the company wants to compare the delivery times. The company plans to make several different types of shipments to its branch office. To compare the carriers, each shipment will be sent in triplicate, one with each carrier. The results listed in the table are the delivery times in hours.

Shipment Carrier A Carrier B Carrier C
1 15.4 16.8 17.3
2 14.7 16.6 16.8
3 14.8 15.7 15.8
4 15.2 16.4 17.2
5 14.6 15.9 15.6

Is there evidence of a difference in mean delivery times among the three carriers?

Please see attached for full question.

#### Solution Preview

The question here is to compare the population means of the 3 carriers using ANOVA.
The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different:
H0: D1=D2=D3 vs.
H1: at least one D is different

The grand mean of a set of samples is the total of all the data values divided by the total sample size. Dgm= 15.92
The total variation (not variance) is comprised of the sum of the squares of the differences of each mean with the grand mean. There is the between group variation and the within group variation. The whole idea behind the analysis of variance is to compare the ratio of between group variance to within group variance. If the variance caused by the interaction between the samples is much larger when compared to the variance that appears within each group, then it is because the ...

#### Solution Summary

The solution uses an explanation of 600 words to describe how to find whether there is evidence of a difference in mean delivery times. An Excel file summarizing the calculations is also attached.

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