Using Statistics to Analyze a Scenario

Scenario: You are interested in researching a new ambulance dispatching method. The new method is supposed to be more efficient and uses half the communications personnel of the old method, saving over $300,000 annually. You want to know how the new method compares to the old method in terms of how many minutes it takes ambulances to get to dispatched calls, since you are not willing to switch if the new method increases the dispatch time significantly. For the research study, calls are randomly assigned to one dispatch method or the other. The Old and the New methods are then to be compared. Your level of significance is set at p=.05. You measure the dispatch time on the next 500 calls. At the completion of the study, you obtain the following results for the comparison of the two methods.

Results:
- The p value you obtain is p = .061.
- Mean dispatch time "Old" method=2.5 minutes.
- Mean dispatch time "New" method=2.8 minutes.
- Mean difference .3 minutes.
- 95% CI of difference -.5 to + 1.1 minutes.

Complete the following exercises based on this scenario. Use only 1-2 sentences to answer each question!
1. Write a potential null hypothesis for the study.
2. Write a potential non-directional alternative hypothesis for the study.
3. Write a potential directional alternative hypothesis for the study.
4. Do the two dispatch methods differ significantly? How do you know?
5. Based on your result in #4, which dispatch method should you use? Why?
6. If the true situation is that the two methods do not differ significantly (null is true) and your research shows that the "Old" method is significantly faster, (reject null), what type of error have you made? What are the potential consequences in this case?
7. If the true situation is that the "Old" method is significantly faster (null is false) and your research shows that the two methods do not differ significantly (accept null), what type of error have you made? What are the potential consequences in this case?