# Report on research of increased shipping damage costs

The company has been experiencing increased shipping damage costs. Your team has been instructed to conduct a two-sample test to determine if shipping damages are equal for packages equal to or below 15 pounds (Package A) vs. packages greater than 15 pounds (Package B).

The CEO must report to the Board of Directors if the target delivery time was achieved.

Data available after a 6 month test:

a) The mean shipping damage for Package A was $25.16 with a standard deviation of $2.11.

b) The mean shipping damage for Package B was $29.16 with a standard deviation of $4.65.

c) The sample size is equal for both samples. n = 36

d) Unknown population variances, assumed equal (t test)

The CEO is expecting the following in a professional report:

1. Describe the size and type of the sample needed to complete the project. (refer to RES 341)

2. Clearly written verbal hypothesis.

3. Clearly stated numerical hypothesis

4. Will the research project require a directional test? (i.e., one-tail, two tail)

5. What is the selected level of significance your team has chosen? Why? What is the critical value associated with the chosen level of significance?

6. What is the value of the test statistic?

7. Conclusion

** State and show your work for all 5 steps of the two-sample testing process. The use of Excel is allowed

** Insert a graphical representation of your test

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#### Solution Preview

Please see the attached files.

Five- Step Test procedure

1. The null hypothesis to be tested is "the average shipping damage costs for the two types of packages are equal" against the alternative hypothesis "average shipping damage cost for the two types of packages are not equal".

i.e. The null hypothesis to be tested is ; Alternative hypothesis

where denotes the average shipping cost for package A and denotes the average

shipping cost for package B.

2. The significance level of the test is α = 0.05.

3. The test statistic is given by , where and denote the sample means of ...

#### Solution Summary

A report on research of increased shipping damage costs are examined.