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Name: Institution affiliation: Date: Statistical testing (inferential statistics) Introduction A statistical test provides a mechanism from which quantitative decisions about research are made. The main reason behind carrying out a statistical test is to determine whether there is substantial evidence which is convincing enough to either reject or accept either the null or the alternative hypothesis. As a general rule by not rejecting the null hypothesis it shows there is a reason for us to continue believing it is true.it might also show that there might not be enough data to prove what is being tested. On the other hand the alternative hypothesis which most of the times argues in the affirmative is usually determined using the available data to show that there is enough evidence to link the test being carried out with the assertions put forward. In this study the relationship between how often the internet and it is quite “unlikely" that any observation with such an extreme test statistic t* mainly in the direction of the alternative hypothesis (HA) in case the null hypothesis is true. Therefore based on the initial assumption that the null hypothesis is true it is must be incorrect. The observation is based from the fact that the P-value which is equal to 0.0127 is less than α = 0.05 we therefore reject the null hypothesis H0: μ = 60 and accept the alternative hypothesis HA: μ > 60.Therefore there is no relationship between how often the internet and the physical library are accessed by the students. References Busk P. L. & Marascuilo L. A. (2015). Statistical Analysis in Single-Case Research. Single-Case Research Design and Analysis (Psychology Revivals): New Directions for Psychology and Education 159. Wasserstein R. L. & Lazar N. A. (2016). The ASA's statement on p-values: context process and purpose. [...]

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i have done part one and two, just need part three to be done. in four pages. Due tomorrow at 8 pm Project Part III: Statistical Testing (Inferential Statistics) (38 points total) 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. See www.howardcc.edu (Links to an external site.)Links to an external site. for instructions on avoiding plagiarism in academic writing. This section should be 1-2 paragraphs in length. **If you are struggling to obtain reasonable research – please consult with an HCC librarian. **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). 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. Indicate how you arrived at your results using that technology (i.e. give instructions, indicate the inputs, present screenshots if applicable). 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. Show how you arrived at your results using that technology. 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? Grading Rubric: Part III will be graded by components according to the following guidelines with comments provided to students. Research (4 points total) 4 Points 3 Points 2 Points 1 Point 0 Points External resource is clearly identified and explained. Proposed guess for the true population mean is justified and consistent with the external reference used. Research findings are based on legitimate sources and are referenced appropriately in-text and/or using footnotes and a reference page. Response is well-written, easy to understand, and uses correct statistical terminology. Proposed guess for the true population mean is consistent with the external reference, but some details are missing. Research findings are based on somewhat legitimate sources and are referenced appropriately. Response is at times difficult to understand, or at times uses statistical terminology inappropriately. Some evidence of external research is present. However, proposed guess for the true population mean is inconsistent with the research findings or is not explained and/or justified. Referencing skills need work. No evidence of external research or research is not referenced at all. No submission, submission is plagiarized, or submission does not match assignment. Sampling Distribution (SQR Criterion #2: 4 points total) Must identify the Sampling Distribution of the Mean and use this Sampling Distribution to find the probability of obtaining the sample mean (or more extreme) by chance. 4 Points 3 Points 2 Points 1 Point 0 Points Sampling distribution is correctly identified. Uses correct strategy to find the probability of the sample mean and expresses answers correctly. Diagram is included and is correct. Sampling distribution is correctly identified. Uses correct strategy but makes minor mistakes in finding or expressing answers (e.g. the probability of the sample mean). Diagram is missing or is inaccurate. Uses incorrect strategies OR Uses correct strategy but problem solving process contains inaccuracies (such as sampling distribution not being correctly identified or other major conceptual or procedural errors). Cannot determine any strategy to solve the problem. No submission, submission is plagiarized, or submission does not match assignment. 1-Mean Hypothesis Test and 1-Mean Confidence Interval – SQR Criterion #1: Communicates mathematical and/or scientific concepts using appropriate symbols, notations and vocabulary. (4 points) 4 Points 3 Points 2 Points 1 Point 0 Points Hypotheses, checking assumptions, procedural steps, explanations, and conclusions use appropriate vocabulary, symbols, and notation with no errors. Hypotheses, checking assumptions, procedural steps, explanations, and conclusions use appropriate vocabulary, symbols, and notation with no significant mistakes and/or with minimal inaccuracies. Hypotheses, checking assumptions, procedural steps, explanations, and conclusions make poor or incorrect use of vocabulary or contains many errors. Hypotheses, checking assumptions, explanations, and conclusions are absent. No use of statistical vocabulary and/or notation. No submission, submission is plagiarized, or submission does not match assignment. 1-Mean Hypothesis Test and 1-Mean Confidence Interval – SQR Criterion #2: Applies appropriate process to solve the given problem. (4 points) 4 Points 3 Points 2 Points 1 Point 0 Points Hypothesis test and confidence interval computations use correct strategy to find and express answers correctly. Hypothesis test and confidence interval computations use correct strategy but makes minor mistakes in finding or expressing answers. Hypothesis test and confidence interval computations use incorrect strategies OR Uses correct strategy but problem solving process contains inaccuracies. Cannot determine any strategy to solve the problems. No submission, submission is plagiarized, or submission does not match assignment. 1-Mean Hypothesis Test and 1-Mean Confidence Interval – SQR Criterion #3: Analyzes, evaluates, justifies and interprets the reasonableness of a solution. (4 points) 4 Points 3 Points 2 Points 1 Point 0 Points Conclusions demonstrate accurate evaluation and interpretation of the results of the hypothesis test and confidence interval. Confidence interval results are used effectively to justify the reasonableness of the results of the hypothesis test and to form thoughtful and insightful conclusions. Conclusions demonstrate accurate evaluation and interpretation of the results of the hypothesis test and confidence interval. Confidence interval results are used to justify the reasonableness of the results of the hypothesis test. Some nuances in interpretation may be missed. Conclusions demonstrate insufficient or incorrect evaluation or interpretation of the results of the hypothesis test and/or confidence interval. Confidence interval results are not correctly used to justify the reasonableness of the results of the hypothesis test. Conclusions are not justified and/or results of the hypothesis test or confidence interval are not interpreted correctly. No submission, submission is plagiarized, or submission does not match assignment. Effective Use of Technology -- TC Criterion #2: Using, adapting or designing technologies to achieve the best results for research, communication or task-related objectives (4 points) 4 Points 3 Points 2 Points 1 Point 0 Points Multiple, complementary technologies utilized to yield outstanding results, demonstrating advanced command of each of the tools. Multiple technologies used appropriately to complete project tasks in a manner sufficient to meet project goals, demonstrating proficiency in utilizing multiple tools. Project utilizes some technology, but does not completely or consistently meet project goals. No technology used. No submission, submission is plagiarized, or submission does not match assignment. Discussion (10 points) A complete response should address: statistical and practical significance, which type of error could have occurred, and a thorough exploration of limitations including the impact of sampling issues and how well the test/interval conditions were met. 10 Points 8 Points 6 Points 4 Points 2 Points 0 Points All questions are answered completely. Responses are well-written, easy to understand, and use correct statistical terminology. Discussion of significance, type and sources of error, and research limitations is thoughtful, correct and/or reasonable and demonstrates an excellent grasp of statistical concepts. All questions are answered. Responses are fairly well-written, and use mostly correct statistical terminology. Discussion of significance, type and sources of error, and research limitations is mostly correct/ reasonable but may contain minor errors and demonstrates a good grasp of statistical concepts. Most questions are answered. Responses at times contain errors, are difficult to understand, and/or use incorrect statistical terminology. Discussion of significance, type and sources of error, and research limitations are mostly correct/ reasonable and demonstrates a fair grasp of statistical concepts. Several questions were left unanswered or responses contain major errors. Response demonstrates a limited grasp of statistical concepts. Most questions were left unanswered or responses are largely incorrect or do not make sense. Response demonstrates a lack of understanding of the relevant statistical concepts. No submission, submission is plagiarized, or submission does not match assignment. Professionalism (3 points) 3 Points 2 Points 1 Point 0 Points Report is highly professional in appearance, typed using an appropriate mathematical typesetting program, easy to read/comprehend, and complete. Report demonstrates some professionalism, but contains distracting errors/problems in typesetting. Formatting/organization, vocabulary, and/or grammar need attention. Report demonstrates some professionalism, but problems with organization, typesetting, and/or grammar make it difficult to read. Report does not demonstrate appropriate professionalism as required by the assignment. Completeness (1 point) 1 Point 0 Points All required sections are present. Parts I and II are included in the final project submission and are compatible (they all relate to one another). Project is missing Parts I and II or other major sections. OR No submission / submission is plagiarized. Rubric MATH-138 Project III (AY15-16 GenEd) MATH-138 Project III (AY15-16 GenEd) Criteria Ratings Pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.01 view longer description threshold: 3.0 pts 4.0 pts External resource is clearly identified and explained. Proposed guess for the true population mean is justified and consistent with the external reference used. Research findings are based on legitimate sources and are referenced appropriately in-text and/or using footnotes and a reference page. Response is well-written, easy to understand, and uses correct statistical terminology. 3.0 pts Proposed guess for the true population mean is consistent with the external reference, but some details are missing. Research findings are based on somewhat legitimate sources and are referenced appropriately. Response is at times difficult to understand, or at times uses statistical terminology inappropriately. 2.0 pts Some evidence of external research is present. However, proposed guess for the true population mean is inconsistent with the research findings or is not explained and/or justified. Referencing skills need work. 1.0 pts No evidence of external research or research is not referenced at all. 0.0 pts No submission, submission is plagiarized, or submission does not match assignment. 4.0 pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.02 view longer description threshold: 3.0 pts 4.0 pts Sampling distribution is correctly identified. Uses correct strategy to find the probability of the sample mean and expresses answers correctly. Diagram is included and is correct. 3.0 pts Sampling distribution is correctly identified. Uses correct strategy but makes minor mistakes in finding or expressing answers (e.g. the probability of the sample mean). Diagram is missing or is inaccurate. 2.0 pts Uses incorrect strategies OR Uses correct strategy but problem solving process contains inaccuracies (such as sampling distribution not being correctly identified or other major conceptual or procedural errors). 1.0 pts Cannot determine any strategy to solve the problem. 0.0 pts No submission, submission is plagiarized, or submission does not match assignment. 4.0 pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.03 view longer description threshold: 3.0 pts 4.0 pts Hypotheses, checking assumptions, procedural steps, explanations, and conclusions use appropriate vocabulary, symbols, and notation with no errors. 3.0 pts Hypotheses, checking assumptions, procedural steps, explanations, and conclusions use appropriate vocabulary, symbols, and notation with no significant mistakes and/or with minimal inaccuracies. 2.0 pts Hypotheses, checking assumptions, procedural steps, explanations, and conclusions make poor or incorrect use of vocabulary or contains many errors. 1.0 pts Hypotheses, checking assumptions, explanations, and conclusions are absent. No use of statistical vocabulary and/or notation. 0.0 pts No submission, submission is plagiarized, or submission does not match assignment. 4.0 pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.04 view longer description threshold: 3.0 pts 4.0 pts Hypothesis test and confidence interval computations use correct strategy to find and express answers correctly. 3.0 pts Hypothesis test and confidence interval computations use correct strategy but makes minor mistakes in finding or expressing answers. 2.0 pts Hypothesis test and confidence interval computations use incorrect strategies OR Uses correct strategy but problem solving process contains inaccuracies. 1.0 pts Cannot determine any strategy to solve the problems. 0.0 pts No submission, submission is plagiarized, or submission does not match assignment. 4.0 pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.05 view longer description threshold: 3.0 pts 4.0 pts Conclusions demonstrate accurate evaluation and interpretation of the results of the hypothesis test and confidence interval. Confidence interval results are used effectively to justify the reasonableness of the results of the hypothesis test and to form thoughtful and insightful conclusions. 3.0 pts Conclusions demonstrate accurate evaluation and interpretation of the results of the hypothesis test and confidence interval. Confidence interval results are used to justify the reasonableness of the results of the hypothesis test. Some nuances in interpretation may be missed. 2.0 pts Conclusions demonstrate insufficient or incorrect evaluation or interpretation of the results of the hypothesis test and/or confidence interval. Confidence interval results are not correctly used to justify the reasonableness of the results of the hypothesis test. 1.0 pts Conclusions are not justified and/or results of the hypothesis test or confidence interval are not interpreted correctly. 0.0 pts No submission, submission is plagiarized, or submission does not match assignment. 4.0 pts This criterion is linked to a Learning Outcome GE.TC.MATH138.02 view longer description threshold: 3.0 pts 4.0 pts Multiple, complementary technologies utilized to yield outstanding results, demonstrating advanced command of each of the tools. 3.0 pts Multiple technologies used appropriately to complete project tasks in a manner sufficient to meet project goals, demonstrating proficiency in utilizing multiple tools. 2.0 pts Project utilizes some technology, but does not completely or consistently meet project goals. 1.0 pts No technology used. 0.0 pts No submission, submission is plagiarized, or submission does not match assignment. 4.0 pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.08 view longer description threshold: 8.0 pts 10.0 pts All questions are answered completely. Responses are well-written, easy to understand, and use correct statistical terminology. Discussion of significance, type and sources of error, and research limitations is thoughtful, correct and/or reasonable and demonstrates an excellent grasp of statistical concepts. 8.0 pts All questions are answered. Responses are fairly well-written, and use mostly correct statistical terminology. Discussion of significance, type and sources of error, and research limitations is mostly correct/ reasonable but may contain minor errors and demonstrates a good grasp of statistical concepts. 6.0 pts Most questions are answered. Responses at times contain errors, are difficult to understand, and/or use incorrect statistical terminology. Discussion of significance, type and sources of error, and research limitations are mostly correct/ reasonable and demonstrates a fair grasp of statistical concepts. 4.0 pts Several questions were left unanswered or responses contain major errors. Response demonstrates a limited grasp of statistical concepts. 2.0 pts Most questions were left unanswered or responses are largely incorrect or do not make sense. Response demonstrates a lack of understanding of the relevant statistical concepts. 0.0 pts No submission, submission is plagiarized, or submission does not match assignment. 10.0 pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.09a view longer description threshold: 2.0 pts 3.0 pts Report is highly professional in appearance, typed using an appropriate mathematical typesetting program, easy to read/comprehend, and complete. 2.0 pts Report demonstrates some professionalism, but contains distracting errors/problems in typesetting. Formatting/organization, vocabulary, and/or grammar need attention. 1.0 pts Objective - Report demonstrates some professionalism, but problems with organization, typesetting, and/or grammar make it difficult to read. 0.0 pts Report does not demonstrate appropriate professionalism as required by the assignment. 3.0 pts This criterion is linked to a Learning Outcome CO.MATH138.CAPSTONEIII.10 view longer description threshold: 1.0 pts 1.0 pts Meets Objective - All required sections are present. Parts I and II are included in the final project submission and are compatible (they all relate to one another). 0.0 pts Does Not Meet Objective - Project is missing Parts I and II or other major sections. OR No submission / submission is plagiarized. 1.0 pts Total Points: 38.0

Subject Area: Statistics

Document Type: Dissertation Proposal