STAT225 Summer 2014Final ProjectThere are a possible 100 points on this final project. The final project is worth 24% of your final grade.The final project is due on July 13, 2014. There will be no extensions or opportunity to revise on this assignment. Please make sure you have posted this work to your Assignments Folder by midnight on Sunday, July 13, 2014. You may post your Final Project as an attachment in your Assignments Folder.If you have any questions about this assignment, please post them to the Questions about the Final Project main topic within the Final Project conference. Description of the ResearchAt the University of Mytholopolois the head of the statistics department wants to find out whether or not 7 basic topics are being adequately learned in introductory statistics courses. A test is written that has 7 questions, one question addressing each of the main topics under consideration. These topics are: 1 – measurement scales2 – measures of central tendency3 – standard deviation4 – normal curve and empirical rule5 – t-tests6 – ANOVA7 – correlation and regressionThis brief test is going to be administered to all students registered in the introductory statistics course at the beginning of the first session and the end of the last session. This is a pre-test/post-test design. But before this full scale data collection effort begins the department is going to test this little instrument. Eight students are selected to use as a test group. The following is a table of the student scores in the pre-test condition and the post-test condition, along with some other important information.This final project is asking you to consider 4 different statistical tests. The first is what the department head is looking for, the second is an extension of that with a further breakdown of information, the third is looking for a relationship between two different variables and the fourth is asking what test you would use to predict a students score. Student Sex Pre-test Post-test Hours per week studying statisticsHope F 4 6 15Franklin M 2 5 18Lily F 4 7 13Paul M 3 6 11Dorothy F 5 5 7Luna F 4 6 12Duncan M 2 5 14Swabby M 6 7 9There is a limited amount of data presented here because I don’t want to overwhelm you with long calculations. Please assume that the distribution is normal.Answer the following questions about this problem. Preliminary information about the data (33 points):Points Question3 points 1. What is the head of the statistics department trying to find out? 4 points 2. What are the data elements (variables) that are being collected by the researcher?4 points 3. What is the measurement scale of the each of the variables of interest?2 points 4. What is the mean of the pre-test scores? What is the mean telling you?2 points 5. What is the median of the post-test scores? What is the median telling you?2 points 6. In both the pre and post test conditions, considering these as a single sample, what is the mode? (There should be 16 values considered.) What is the mode telling you?2 points 7. What is the range of the hours studied? What is the range telling you?3 points 8. Can you calculate a mean for the sex of the students involved in this pilot study? Explain your answer.4 points 9. What is the standard deviation of the pre-test scores? Please show all your work. (You don’t have to do the standard deviation of the post-test scores.)3 points 10. What is the standard deviation telling you about the pre-test scores?2 points 11. State the percentages of the empirical rule.2 points 12. What is the difference between a population and a sample? Be specific and give an example of a single group where in one situation it would be a population and in another situation this same group would be a sample.First statistical test (32 points): Points Question2 points 13. What statistical test are you going to use to find out whether there is a significant difference between the pre-test sample and the post-test sample? Be specific. 3 points 14. Explain why this test is appropriate. Include in your answer three of the assumptions of the test you’re proposing and explain why each is important.2 points 15. What is the null hypothesis for this problem?2 points 16. What is the research or alternative hypothesis for this problem?5 points 17. Perform the calculations for your proposed statistical test and show your work and your answer.2 points 18. What is your observed value? 2 points 19. What are your degrees of freedom? 2 points 20. Is this a one-tailed or two-tailed test? Explain why.2 points 21. What table are you going to use to find your critical value? Please be specific and give the page number from Aron, Coups and Aron.2 points 22. What is your critical value? Your p value should be .05. 2 points 23. Based on your observed and critical values, is the difference between these two groups significant? 3 points 24. What conclusion can you draw from your result? State your conclusion in words, based on your null hypothesis.3 points 25. Describe what a a Type I error and a Type II would be for this particular study. Second statistical test (16 points): In your first statistical test you tried to find out whether or not there was a difference between two groups of test scores, the pre-test and the post-test. What if we wanted to find out if there was a difference between the pre- and post- test scores broken down by sex? Points Questions4 points 26. How many groups are there for this analysis considering pre-test data, post-test data and sex? Name them.2 points 27. What statistical test would propose to find out if there is a difference between these groups?2 points 28. What would your null hypothesis be for this additional analysis? 2 points 29. What would your research hypothesis be for this additional analysis?2 points 30. In general, what conclusion could you draw from that statistical test? 2 points 31. In general, what conclusion can’t you draw from this statistical test? 2 points 32. What additional statistical test do you need to perform in order to find out where the actual difference lies?Third statistical test (15 points):In your first and second statistical tests you were trying to find out whether there was a difference between the way various groups performed on the SAME variable. In this third scenario we want to find out whether there is a relationship between TWO different variables.Points Questions2 points 33. What statistical test do you propose to find out the relationship between post-test scores and the number of hours studied?3 points 34. What formula would you use to find the relationship between the post-test scores and the number of hours studied?4 points 35. Using this formula, what would your result be? Show all your work, please.2 points 36. How would you interpret your result?2 points 37. In general, what can you conclude from this statistical test?2 points 38. In general, what can’t you conclude from this statistical test? Fourth statistical test (4 points):Now, based on the result of the third test, we can conduct a further statistical test in order to see if we can make a suggestion to students about the number of hours they need to study in order to learn the most in their statistics course.Points Question2 points 39. What statistical test can we use to predict the number of hours a student needs to study in order to do well in statistics?2 points 40. Describe in words the interpretation you would be able to make based on this additional statistical test?