Statistics Paper Project

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Mathematics

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The document file offers the descriptions and requirements. If primary data is picked, it should be based on normal college students lives in New York state. If using secondary data, it should be based on ordinary public-known sources. Use of estimations, confidence intervals and hypothesis testing is required. Textbook "Mind on Statistics 5 th edition" could be used as reference. Number of Pages is not strictly required but is preferred in single spaced 4 pages along with charts and diagrams. The images below provides a sample past paper.

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The project is your independent research and data analysis based on either primary (you collect your own) data or secondary (use some existing database, from the internet or elsewhere) data. You are to design the study, collect the data (or use some existing data), analyze the data, draw appropriate conclusions, and document your study in a carefully written report. Reports or papers are preferred over power-point presentations, posters or other forms of presentation. See below for some guidelines on the organization of the final report. One possible plan (but, not necessarily the only one) Start with some hypothesis, conjecture or claim. The claim might be your own or someone else's (for example: a manufacturer that claims their product lasts longer than that of a competitor). Figure out the best way to test this claim. The first step might be to figure out the correct response to measure (ordinal, nominal, interval, ratio, discrete, continuous). Decide on a plan of attack, which might include doing an observational study or a designed experiment. The data to put your claim to a test might be available somewhere (on the Internet?) or you may have to collect it yourself. If you collect the data yourself, decide on an appropriate method of collection (random sample, cluster sample, etc.) and an appropriate sample size. Justify the method you used and the sample size selected. Determine the appropriate analysis to test the claim. Use of descriptive statistics and graphs may be part of the project but will graphs and numbers alone will rarely be adequate. Use of statistical inference (confidence intervals, hypothesis testing, etc.) is highly recommended. Carefully complete the analysis. Draw an appropriate conclusion (if possible) and carefully document what you did and your conclusions. It may also be appropriate to comment on lessons learned and potential improvements if the study was to be repeated (what you might do differently). A project outline or 1 page description of your intended project is due by Midterm. The project outline is NOT required and will not be graded. However, it is highly recommended that you submit one. The outline will be reviewed and returned to you with suggestions and comments for improvement. Therefore, your outline should be as specific as possible. Instead of submitting a proposal, you may discuss your project ideas in person with me during office hours (or by appointment) Projects will be ranked using the criteria shown below. The instructor reserves the right to grant extra credit for a truly exceptional project (rarely done) and to give a failing grade to extremely poor projects. Projects should be done independently. Projects involving collaboration between two or more people will NOT be accepted this semester. Criteria for a "good" Project • Clear statement of the problem (what is the claim? What are you trying to demonstrate?) • Relevance of the problem to real life (why should anyone care?) • Uniqueness/Originality • Clear statement of conclusions (what's the bottom line? what's the decision?) • Justification for: o Sample size o Primary of secondary research/experimental design vs. study of existing data. o Analysis tools used (what did you compute and why did you choose those "statistics") o Sampling method (random, cluster, systematic, etc.) - why and how? • Use of Graphics (if appropriate) • Use of Computer Aids (like MINITAB), if appropriate • Accuracy of calculations (No numerical mistakes) • Neatness • Organization of Final Report. There are no requirements on the length of the project write-up. Make it as short as possible to communicate the important steps in your analysis. Consider writing for an audience that is statistically literate but not a statistical expert. In other words, consider the audience for your report to be an average college student or graduate. Communicate your ideas as clearly as possible. Think Quality, NOT Quantity. Do not include any irrelevant information. Focus on the main problem. Do not include histograms, statistics, etc. that are not relevant to your main thesis. Computer output, equations and detail math calculations rarely adds anything to a report. If these are included, they should be in an Appendix at the end of the report. • Statistical Inference. The emphasis of this course is on statistical inference or inductive logic. The closer your project comes to using these ideas, the higher it will be rated. Tables and graphs are nice but try to use the ideas of estimation, confidence intervals, hypothesis testing (Chapters 6, 7, 8, 9) if you want your project to rate high. For some projects, the problem you choose may require you to go beyond the material covered in class in order to provide an appropriate analysis. If this is the case and you are successful, your project will rank higher. In past semesters, research reports consisting of critiques of journal articles and historical aspects of statistics and/or statisticians were allowed as projects in this course. This type of project will NOT be accepted this semester. Dedication of Yast Comed to instrumentalists Introduction Those who study must know that it is a very competitive field that requires a great deal of time to be went practicing for performances. That being said, I thought it would be interesting to look at which group of music majors is more dedicated vocalists or instrumentalists. Based on my experience as a musie student hypothesized that instrumentalists are more dedicated musicians than vocalists, and conducted a series of tests to prove this claim true, using hours spent practicing per week as the measurement of dedication. Below I have highlighted the results that found, and detailed the exact steps that I took along the way. Practical Significance or Release Knowing what musicians are the most dedicated could be important for those who are casting for a show or hiring for a performance; these individuals want to know that that the musician they hire will be dedicated to preparing for their performance. This knowledge could also be applied to salaries of musicians, with more dedicated musicians receiving a higher pay. Aspiring music students may also find this information useful because it could show them how much they should expect to practice in order to be successful as a vocalist or instrumentalist Procedure: 1. Gathering Data - The very first step was to collect the necessary data to be analyzed. I decided to collect my own data because there was no reliable raw data available that would serve the purpose that I wished it to. In order to gather the data, I put together a survey that asked three questions: a. 1) Are you a vocalist or an instrumentalist? b. 2) How many days per week do you practice? c. 3) How many hours do you spend per practice session? From this I would be able to compute how many hours on average each individual spent practicing each week. This survey was distributed to thirty-five music students, twelve of which were vocalists and twenty-five that were instrumentalists. A survey was used because it was simple to gather the data from my college campus this way, and an experiment was not required to collect this data. The sample size of thirty-five was used because there are not many music students on the River Campus; I gathered just enough data to determine that the sample was normal, representative, and could be successfully analyzed without having to expand my survey to include 1 vhich would have compromised the sample and we study). 2. Numerical Summary and Analysis* - I computed the averages for the individual survey results and from there calculated summary statistics, which I then compiled and summarized for later analysis using box-and-whisker plots and comparative tables (which can be found in the "Reference Tables and Statistics" section of this report). Through this analysis I determined that the mean number of hours that vocalists practice every week is 2.83 with a standard deviation of 2.42 hours, while for instrumentalists the mean hours of practice per week is 7.52 with a standard deviation of 6.42 hours. Right away this gives us a clue that instrumentalists practice more than vocalists, because the difference in mean practice times is (-)4.69 hours. After computing a 95% confidence interval on this difference, I can say with 95% confidence that the difference between these means would lie between (-)1.72 and (-)7.66, which means that this difference of (-)4.69 is most likely accurate and deserves to be looked at more closely. The box-and-whisker plots that I have created show that the data is approximately normal, with no outliers or extreme skewness that could affect analysis, they also show that there is more variability amongst instrumentalists than there is amongst vocalists. From looking at the spread of the data in the box-and-whisker plots displayed below, it is clear that my hypothesis has merit and deserves further testing and analysis. Vocalists Series 1 Series 2 1 Series3 Series4 0 2 4 6 00 Series5 LO 12 14 16 18 20 Instrumentalists Series1 Series2 Series3 Series4 Series5 0 2 4 6 8 10 12 14 16 18 20 *Note: All calculations were made on a TI-84 Plus graphing calculator fo wady could be important for viewing en la promance would why up with others in the field and ple whose med voice parte putere dal parts spend the montering www tepplied in a real worem yere they so you could use this to see how then you should see you are looking to be calls for a show and you non, you may wish to pay them more to come for the end Reference Table and RawData Numerical martes und aatiles 10 25 4 64 25 IGA 175 242 75 3 Test News 225 1 321 015 0.0015 ttestati 2 O 35 D-value 2625 17.5 17.5 4 7.5 17.5 5.25 15 3 1 7.5 Summary Vocalist Minimum 91 0.25 Median 03 425 Maximum 14.5 175 Hypothese Test and State Significance - The final step in determining whether instruments are indeed more dedicated the vocalists was to conduct a hypothesis test. In this case I have used are samples for the difference in two means to determine if there is a statistically significant difference in the data concocted the pode estas follows using a T-54 Plus graphing calor SallAlepothesis: I have signed the sample of vocalists to wl and the instrumentalisto 2. Given this, my mull and strative hypotheses to testare and Hard Sip 2 Yeng Conditions and Coming Test Statistic: This is not a large samples, but it is approximately normal and random, so once these criteria were verified as I went ahead and computed a test statisti-3.21 Step Finding the valu have lected to use a level of significance of .05 because that is the generally accepted value. That being said the p-value that I have calculated for this situation is pm.0015 d. Selising the P.Value to Deemine Slanic and Form Conclusion: The p-value that I have computed is much smaller than the level of significance a which means that it is statistically significant. Given this, it may be reasonable to reject the null hypothesis that the two means are equal in favor of the alternative hypothesis (that) Step 5 Reportin Content Based on the results of this hypothesis test, we can conclude that the mean time spent practicing by instrumentalists is indeed greater than the mean time spent practicing by vocalists in this sample. Summa and Conclusion: The purpose of this study was to see if instrumentalists are more dedicated musicians than vocalists. I set out to do this through determining if there was a statistically significant difference between the lengths of time each group of musicians spends practicing each week on average. In other words, I was trying to prove that the mean practice time for instrumentalists is greater than the mean practice time for vocalists, and that this difference is unlikely to be present in the data due to random chance. I gathered a representative sample of data through a survey sent out to music students at the generated numerical and visual summaries for these two sets of data. Then I found the difference between the means and did a 95% confidence test on that difference to be certain that it was worth further testing. Based on my initial analyses I concluded that the next step should be to conduct a hypothesis test, so I conducted a two sample t-test for the difference in two means to determine if the difference I was seeing in the data was indeed statistically significant. The results of this study showed that the difference in the two means is statistically significant, and therefore it may be reasonable to conclude that instrumentalists are indeed the more dedicated musicians compared to vocalists, the average amount of time that they spend practicing per week is significantly greater than the time spent practicing by vocalists.
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