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Stat 1000 take home exam (100 points)

Work independently on this exam. Do not discuss your answers with others.  Label your answers part A and part B. Create a numbered list where your answers will correspond to the numbered prompts below under both part A (1-10) and part B (1-10). Be sure to organize your document as specified. Keep your answers brief and to-the-point. This will be graded on quality not quantity.

Part A. 50 points.

Are one’s beliefs about getting covid associated with vaccine hesitancy. This data is adopted from a larger study published in the fall of 2020. In this subset, participants responded if they intended to be vaccinated and if they believed  they would get COVID. The data is summarized in the table below.

Belief about getting Covid

Intent to Be Vaccinated

Yes

No or Not Sure

I don't think I will get the coronavirus

327

295

I think I will get a mild case of the coronavirus

173

90

I think I will get seriously ill from the coronavirus

44

14

Answer the following. Please number your answers to match the numbers in the prompts below. You should use software to do this analysis. Each prompt below is worth 5 points.

1. State your research question in a sentence. Also, write out both the null and alternative hypotheses in separate statements.

2. What type of statistical test will be performed (be specific, e.g. matched pairs, two independent sample t, chi-square goodness of fit test, chi-square test of association, ANOVA, etc.). How did you decide what type of test to run?

3. What assumptions need to be checked for this test? For each, state if they are met in this study.

4. Provide at least one graph of the data, and some interpretation (a sentence or two) for what the graphs tell us.

5. Conduct the statistical test. What is the test statistic and the degrees of freedom?

6. What was the p-value? Assuming alpha=.05, state the decision.

7. If Ho was rejected, where do we see the largest differences from (e.g. contributions to the test statistic)?

8. In a sentence or two, state your conclusion in layperson’s terms, avoid jargon. Be sure to interpret your results in the context of the research question.

9. If a researcher made a type I error, what would this be in the context of the problem?

10. In a sentence or two, suggest a reasonable follow-up study idea to help to confirm this researcher’s findings. An obvious example would be to repeat the study with a larger sample size. Come up with an idea of your own to look for how beliefs may impact vaccine hesitancy. You are not limited to this data or population for the next study. Answers will vary, feel free to be creative.

Part B. 50 points. Note: this section is independent of part A.

You have the opportunity to do research! Congratulations! You will need to tell me what research question YOU want to answer using the tools we have learned in class. This can be from any field: business, sports, psychology, medicine, mechanics, forestry, anthropology, physics, data analytics, etc. etc. …. any field. Choose a research idea that is of interest to you. A question you would like to answer.

You will have the ability to get a good random sample of up to 1000 subjects (you do not need to ask for this many) but you must specify how EXACTLY you plan to collect your data. Picture a spreadsheet with your data. What does the data look like?

You will use the descriptive methods we have learned in class to explore the data.

You may use one of the following inferential methods for quantitative data: matched-pair t-test, two-independent sample t-test, simple linear regression, or one-way ANOVA.

In this hypothetical situation, answer the following:

1. What is your research question? What is your population of interest? Briefly describe the problem you are trying to solve in a sentence or two.

2. Clearly state Ho and Ha.

3. How will you collect the data? Be specific about where the data in your spreadsheet will come from – how is the researcher collecting the data? What does the sample look like?

4. Provide a mock-up (screenshot or photo) of the first few rows of your data worksheet. Explain every column of data that appears in your spreadsheet. Be sure to include if the data in that column categorical or quantitative?

5. How will you graph your data? Explain why you chose the graph(s) you did.

6. What numerical summaries will you use to describe your data (descriptive statistics)?

7. Which statistical test will you use to test your hypotheses?

8. What alpha level are you going to use? Why? In your own words, explain what the alpha level means.

9. How will you make sure your test has enough power? In your own words, explain what power means.

10. If you reject Ho, what will your conclusion be in the context of your research question?