### Discuss the confidence interval: What is the confidence interval? State the plausible range of differences between the two populations.

Statistics

**Math 109 Project Part 2**

**Description:** For this semester-long project, you will collect and compare quantitative data from two populations. You will use statistical methods to determine if there a difference between the means of the two populations.

You will present your results and conclusions for this second part of project in an essay format that is at least 800 words in length. Do NOT include definitions or state how to calculate results in your project. State your findings and conclusions in your own words.

**Discussion of Topic (Total: 4pts)****
**• Give a clear and concise overview of the topic chosen for the project: This should be basically the same as the Discussion of Topic from Part I. Introduce your topic and why it was interesting to you. You can copy and paste your introduction from part I of the project, just make sure that you hadn’t lost any points for it the first time around. This section should be at most 1 short paragraph.

**Discussion of Part 1 (Total: 5pts)****
**• Summarize methods from part 1: What were some of the methods you used in part one to compare shape, center, and spread? Comment briefly about your visual comparison of the samples.

• Summarize conclusions from part 1: What was the answer to your main overarching question that you came to by the end of part one? Did you decide the populations were likely about the same, or did you decide that the two populations were different?

• Describe how confident you were in your conclusions from part 1: Do you feel like your samples led you to accurate conclusions? What are some things you know about your samples and this project that you feel make your data good, and what are some things you know that make your data unreliable?

• This section should be at most 1 paragraph.

**Discussion of Hypothesis Statement (Total: 4pts)****
**• State the null and alternative hypothesis in symbol form: Provide the symbol form of your null and alternative hypotheses for the two-tailed test testing if there is a difference between the population means.

• State the null and alternative hypothesis in sentence form: Interpret the symbol form of the hypotheses in the context of the project. Use specifics about your specific data and populations.

**Discussion of Hypothesis Test Results (Total: 12pts)**

- Provide a clear analysis of the hypothesis test results: What does it mean to run a ‘two- tailed’ test? What is the test statistic? What is the P-value?

• State your conclusion and support the decision: Given your test results, do you reject or fail to reject the null hypothesis? How did you (mathematically) come to that conclusion?

• Discuss what the conclusion means for the two populations: Interpret your conclusion in the context of the project. Use specifics about your populations. Based on your conclusion, what is the answer to the main overarching question? Are your population means the same or different?

• Discuss if the results of the hypothesis test match the previous conclusions from part 1 of the project: Go back to your conclusions from part 1. Is it the same conclusion? It is okay if it is different. Just compare the two conclusions. If the conclusions are different, which is more reliable?

**Discussion of Confidence Interval (Total: 12pts)****
**• Discuss the confidence interval: What is the confidence interval? State the plausible range of differences between the two populations.

• Interpret the confidence interval: What does your confidence interval represent in the context of the project? Are the population means the same or different? Is one likely larger than the other? How do you know?

• Discuss if the values make sense: Do these values seem reasonable to be the differences between your population means? Does the interval seem too wide or narrow to be reasonable?

**Comparison of Hypothesis Test and CI (Total: 6pts)****
**• Compare the results of the Hypothesis Test and Confidence Interval: You had to answer the main question: “Are the population means the same or different?” based on hypothesis test and also based on your confidence interval. Did you come to the same conclusion?

**Discussion of Expectations (Total: 4pts)**

- Briefly discuss what the expectations were at the beginning of the project: When you chose your topic, what did you think the result would be?

• Discuss how the analysis has supported or changed any initial thoughts: Did your results from part 1 support your original expectation? Did your results from part 2 support your original expectation? Now that you have completed the analysis, was your original expectation right or wrong?

**Discussion of Possible Changes (Total: 4pts)****
**• Clearly discuss any changes that could be made if the project was to be redone: Imagine that you are a real statistician. What would you change about your project? Think about the things you know about your project topic and data collection that make your analysis accurate or inaccurate. How would you improve on those methods, what mistakes would you want to correct?