Statistical Testing (Inferential Statistics)

: Statistical Testing (Inferential Statistics) In this section you will expand your project to explore inferential statistics for ONE of your quantitative variables: the one you decided in Part II was more nearly normal than the other. This section will include some external research, hypothesis testing and confidence intervals, and a discussion of hypothesis testing errors and issues. Your project should be submitted as a professional report including everything from Part I and II using the following headings: Research Proposal: all sections from Part I Data and Descriptive Statistics: all sections from Part II *** IF you did not do Part I: you must at a minimum obtain approval from your instructor on your variables and collect data. *** IF you did not submit Part II: you can still submit Part III but will lose completeness points for any missing sections. Part III: Statistical Testing -- Research: Remind your reader which quantitative variable you considered most “nearly normal” in distribution and conduct some external research using the internet, library, or other academic sources to propose a reasonable guess for the true population average (mean) and standard deviation for your variable of interest. Be sure to remind your readers what population of interest you are referring to: for example, are you limiting your consideration to adult U.S. citizens, adults worldwide, U.S. college students, dogs owned as pets, etc. Describe the study/resource and why the proposed values are reasonable estimates for the population parameters (true mean and standard deviation). Cite your sources appropriately using APA style in-text citations or the Chicago Manual of Style footnotes and add a "References Sheet" on the last page. for instructions on avoiding plagiarism in academic writing. This section should be 1-2 paragraphs in length. . **If you are able to obtain information about a plausible population mean but not a standard deviation, please use your sample standard deviation as an estimate. Sampling Distribution: Recall that the sampling distribution of means for a nearly normal variable should be Normal, with a mean equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of your sample size. Naturally the true population parameters (mean and standard deviation) for your variable is unknown, however you identified a reasonable estimate in the section above. Based on these estimates, give the sampling distribution model that applies to your variable. Then use this sampling distribution to find the probability of seeing your data (sample mean) or more extreme by chance. Explain every step of your work and include a diagram of the sampling distribution normal curve and your observed sample statistic (use appropriate technology). One Sample Inferential Statistics: Suppose you suspect that the population mean found through your research is inaccurate and want to test the hypothesis that the population mean has changed (is different from the population mean found in your research). Since you are using quantitative data, you will be doing a 1 Mean Hypothesis Test (T-Test). You MUST do the following: 1-Mean Hypothesis Test • Write your hypotheses using appropriate notation. • Evaluate whether or not the conditions are met for you to conduct your test (you must actually verify all conditions – include diagrams or computations as applicable). o If your conditions are NOT met, you can proceed but you MUST discuss the implications of not having met conditions in your Discussion section. • Use technology to conduct your test and professionally present your results. o Indicate how you arrived at your results using that technology (i.e. give instructions, indicate the inputs, present screenshots if applicable). o Present your results. • Write a conclusion to your hypothesis test in the context of your research question using appropriate statistical terminology 1-Mean Confidence Interval • Use technology to create a 95% confidence interval for the true population mean. o Show how you arrived at your results using that technology. o Respond to the question: Are the results of your confidence interval consistent with your hypothesis test? Why or why not? Discussion: Provide a detailed discussion of the potential issues and limitations of the results of your research into this one variable. Your discussion should answer all of the following questions (at a minimum!): • How confident are you that your results are accurate and meaningful? Are your results statistically significant? How about practically significant (you’ll need to refer to your confidence intervals to answer this question). • What limitations should someone consider when looking at your research; for example: how well did the T-Test model apply to each test (how well were the conditions met) and how representative were your data. • Discuss which potential error could have occurred in your research: Type I or Type II error and what it means in the context of your scenario. Suggest some possible reasons that this error might have occurred and what consequences might result from this error. • What other problems do you see with your research that might limit how well your research generalizes to the greater population?