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Using Statistics to Analyze a Scenario

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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?

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Solution Preview

1. Null Hypothesis: The mean dispatch time for the new method is equal to that of the old method.
2. Alternative Hypothesis: The mean dispatch time for the new method is not equal to that of the old method.
3. Alternative ...

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Does lecithin enhance memory? To test this idea, nine pairs of people matched in terms of age, sex, IQ and neurological status are given capsules containing either lecithin or a placebo at meals for a week. All are scored on a recent memory talk. A higher score indicates better task performance.

pair lecithin Placebo
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a. Conduct and interpret the appropriate analysis to determine if lecithin significantly improved memory.
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d. After review of the scoring and assessment tool, researchers decided that equal intervals could not be assumed, and that the data should be treated as a rating. Conduct and interpret the appropriate analysis to determine if the lecithin group has significantly better memory.

2. An instructor asks students in his class to indicate whether or not they agree with the opinions of three different speakers.

Speaker 1 Speaker 2 Speaker 3
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a. Conduct and interpret the appropriate analysis to determine if there is a connection between the speaker and the opinion of the students.

3. Suppose that a sociologist determines from the census report that the distribution of people in various occupations in a specific geographic area are as follows:
Agricultural
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Local/state or federal government
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He samples individuals who are members of a particular political party to see if the distribution of occupations are the same.
Agricultural
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Local/state or federal government
Professional and/or self-employed
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310
305
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4. A researcher was interested in the attitudes towards equal rights among stay at home moms and women with jobs outside the home. She creates a survey that measures attitudes toward equal rights, administers it to a sample of 20 women. However, since the survey is not standardizes, she realizes that the scores may not reflect equal intervals.

Stay at Home Jobs Outside the Home
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