PAT (Pre-Admission) SCORES FOR 6 COLLEGES COLLEGE 1 Gender Verbal Math F F M M M M F M F F M F F M M M F M F M M M F F F M M F F M F F M F M F F F M M M M M M M F F F F F 450 640 590 400 600 610 630 660 660 590 580 500 480 530 690 480 450 650 620 630 490 560 710 360 590 520 510 630 740 680 660 690 540 670 580 600 600 710 640 490 650 580 710 740 510 650 580 600 670 640 450 540 570 400 590 610 610 570 720 640 650 540 360 520 640 570 420 650 600 740 520 620 720 390 530 630 600 630 760 690 700 750 560 520 720 560 560 640 650 590 680 710 730 700 560 760 660 640 700 670 COLLEGE 2 Gender Verbal Math F F M F M M F M F M M M M M M M F F M M M F M F M F M M M F M M M M F F M F F F F F M F M M M F F F 370 620 680 620 590 430 680 650 650 660 640 460 430 460 800 310 510 770 750 580 410 430 630 630 480 420 800 650 580 560 670 610 510 560 770 530 650 730 690 610 710 730 450 400 700 580 600 630 600 630 460 470 650 620 690 540 740 650 680 700 680 680 480 600 720 530 550 700 670 630 390 400 680 630 550 430 650 500 690 540 760 740 610 530 690 430 740 790 640 510 680 590 570 410 620 660 670 690 640 700 COLLEGE 3 Gender Verbal Math M F F F F M M M M F F M M F F M M F F F F M F F F F F F F M F M F M M M F M F M F F M M M M F F M F 690 630 480 680 650 460 560 610 620 590 390 510 450 520 470 690 510 770 520 550 680 740 660 740 730 560 570 560 670 650 690 610 500 560 640 430 700 620 610 580 730 520 540 640 680 580 640 700 600 540 740 560 500 630 680 410 560 760 650 640 440 530 440 690 410 620 540 710 570 600 580 700 690 640 680 630 530 540 520 710 700 740 650 700 650 490 570 670 640 640 570 530 580 610 720 490 630 650 630 510 COLLEGE 4 Gender Verbal Math F F M F F M F F M M M F F M F M M F M F M F F M F M M M F M F M M M F F M F F M M M M F M M F M F PERM14D-k M 480 710 650 640 370 710 630 590 750 600 610 490 680 520 680 650 600 550 490 530 560 630 510 710 550 690 700 540 280 710 640 600 610 680 520 730 510 620 530 550 590 620 640 490 530 560 710 480 490 460 540 700 780 570 410 700 660 580 800 690 550 800 610 540 660 700 560 560 390 530 560 590 520 740 560 620 700 620 500 760 710 590 670 670 470 740 680 740 500 680 670 640 570 530 580 600 700 530 490 560 COLLEGE 5 Gender Verbal Math F M M F F M F F F F M M M M M M F M F F F M M M M F M F M M M F F F M M M F F M F F M M F F F M F F 630 510 600 550 670 560 600 650 630 440 650 690 360 510 610 700 540 600 610 700 490 390 580 760 730 590 640 610 760 570 700 630 530 490 600 580 710 600 560 570 630 640 550 690 530 580 550 690 420 Page 6902 520 520 610 570 580 520 600 530 610 470 560 670 290 510 570 740 490 670 710 570 560 630 530 760 760 620 740 620 700 630 740 630 670 700 660 760 700 450 590 690 610 570 600 670 490 640 560 740 410 720 COLLEGE 6 Gender Verbal Math F F F M M F M F M F M M M M M F M M M F M M F F F M M M F M F M M M M M F F F F F F M F F M M F M M 560 560 490 430 690 600 700 630 620 550 600 450 690 590 760 650 540 580 670 650 660 500 610 580 570 690 570 600 540 640 680 730 610 500 580 620 570 690 610 630 540 760 470 340 480 690 620 710 440 400 570 560 510 570 670 550 630 710 610 550 670 610 680 600 580 600 630 530 650 680 660 580 510 500 620 620 540 670 670 760 600 670 550 550 630 710 630 610 570 570 660 690 470 450 500 760 610 630 740 710 1/11/2016 MAT 150-Dr. Kistler Project Spring 2016 This exam has 100 points total and is designed to give you an experience of actually \"doing\" some statistics. Please be neat with your work. You will be graded on the narrative (your understanding) of the data as well as the correct methodology. You should use StatCrunch to do calculations, print graphs and tables as well as perform statistical tests. These instructions are posted in MLP under Project so if you would like to type in the answers or insert graphs and tables from Stat Crunch that is possible for a more polished product. There are many Youtube videos to help you with Stat Crunch. Simply search for what you want to do. I expect a \"professional\" presentation as if I were your supervisor and you were presenting me with information. Label with letters all the portions of each Part. Your variable is: _____________________ The project is due: _____________ When you open Stat Crunch select Stat Crunch Website. Select the Explore option and Data. In a search box to the left put in 150collegedata. All the data for this project will appear in Stat Crunch for you to work with. PART 1 (50 points). You have been assigned a column of data from the PAT scores (Pre-admission Test Scores for Verbal and Math) of 6 Colleges. Use the whole column of data (n=50) as your sample. Do not analyze each section separately. In part I you will be summarizing the results as evidence of your conclusions from other parts. A. Present the data (in a horizontal table sorted). Create an imaginary name for the college you were assigned. Based on the scores you see, what can you say about the type of college or student who goes there? What is the possible relevance of studying this variable? B. Report the mean, median, Q1, Q3, IQR, min, max, as well as standard deviation, variance and range. (In StatCrunch under Stat see Summary Stats) Round appropriately. p. 2 Spring 2016 Project C. Create a stem and leaf (use StatCrunch if possible). Be sure to tell how to read the stem and leaf and report if it has been rounded. D. Create a regular box plot (use StatCrunch if possible). Label the 5 number summary below the graph. E. Show calculations for identifying \"outliers\". Do you have any outliers? What are they? If you have outliers, include a modified boxplot showing the outliers. F. Group the data in 5 classes. Prepare a frequency distribution (a table) showing class limits and frequencies. Be sure to report your class width. G. Create a histogram (use StatCrunch) demonstrating the same 5 classes from the grouped data. Use the same class width as Part F and start at your lowest value. H. Create another appropriate graph for your data. If your data seems to be approximately normal, do a normal probability plot (QQ plot on StatCrunch) to verify. If your data is skewed do a dot plot. I. What is your descriptive summary of this data? What have you learned about the variable? Write 4 paragraphs with a thesis sentence (what you believe to be true about the central tendency, variation, distribution and effects of outliers) and then math evidence to back up your conclusions. Include a paragraph on central tendency using part B above and the graphs as they apply. A summary paragraph is expected on variation; answer the question \"how spread out is the data\". A paragraph talking about distribution should include evidence from graphs and numerical data. A paragraph on outliers should reference your numerical work in part E and the effect the outliers might have on center, variation and distribution. Be sure to reference all calculations that lead you to the conclusions. Make sure you discuss what you observe from all graphs in each of the four paragraphs. p. 3 Spring 2016 Project Part 2 (50 points). How can we use this sample to make inferences? Explain and narrate all parts as directed. A. Explain how this sample meets the requirements of using a t distribution. Mention the degrees of freedom. B. Estimate a 95% confidence interval for the population mean using your data as a sample. Tell what calculator or Stat Crunch command you used. Explain what this interval means. What is the margin of error? Use the point estimate and the margin of error to write a sentence that summarizes this result. C. The average math PAT score is 512 and the average verbal score is 510. Use the appropriate null hypothesis for your set of data. Perform a two-tailed p-value and a classical hypothesis test. Show all five steps for p-value test and the additional steps for the classical test. Use your data as the sample at the = .05 level. Does your result mesh with the result of the confidence interval in part B? Explain how. D. Split the females and males in your sample into two columns. (See StatCrunch/Data/Arrange/Split). Create two boxplots of the comparable measurement of the opposite gender using the same scale. Report the mean and standard deviation for each gender. Comment on the differences you observe (at least a paragraph) between the genders from what you observe in the five-number summaries of the boxplots and the mean and standard deviation. Which gender does better in your variable? E. Is there a difference based on gender? Perform a p-value test and include the additional steps of a classical hypothesis test at the =.05 level with your data comparing males with females. From information gained in the boxplots decide which gender should be list 1 and list 2 in order to perform a right-tailed test. Does an appropriate confidence interval verify your results? Explain. p. 4 Spring 2016 Project F. Is your variable (all 50) correlated with the other variable (math or verbal) from your college. For example, if your variable is College 1 Verbal then you would see if College 1 Math is correlated. DO NOT USE SORTED DATA. Remember each subject has a verbal and a math score and you are seeing if there is a linear relationship. 1. Remove all outliers from both lists. Report what you deleted. 2. Create a scatter plot (Use Stat Crunch) 3. Report the correlation coefficient r. 4. Also compare r with the critical value for n = 50 of .279. 5. What is the coefficient of determination? Explain its meaning. 6. What is the linear regression equation of the paired data? Can it be used to predict scores? Explain.