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Week 3 Lecture Statistics For Decision Making

Week 3 Lecture Statistics For Decision Making. B Heard. Not to be used, posted, etc. without my expressed permission. B Heard. Week 3 Quiz. Your Week 3 Quiz is on material covered in Weeks 1 and 2 Your Week 5 Quiz is on material covered in Weeks 3 and 4

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Week 3 Lecture Statistics For Decision Making

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  1. Week 3 LectureStatistics For Decision Making B Heard Not to be used, posted, etc. without my expressed permission. B Heard

  2. Week 3 Quiz • Your Week 3 Quiz is on material covered in Weeks 1 and 2 • Your Week 5 Quiz is on material covered in Weeks 3 and 4 • Your Week 7 Quiz is on material covered in Weeks 5 and 6 • Your Final Exam is comprehensive covering the material in the three prior quizzes plus the material covered in Week 7 • Your best approach for preparing for the quizzes should be the Practice Quizzes offered in the previous week (for this week’s quiz the Week 2 Practice Quiz) and the live lecture of the Week the actual Quiz is posted Not to be used, posted, etc. without my expressed permission. B Heard

  3. Week 3 Quiz Some Key Thoughts…. Not to be used, posted, etc. without my expressed permission. B Heard

  4. Week 3 Quiz • Name and define and discriminate between the two major branches of statistics (descriptive and inferential). • Define major terms and discriminate between a sample and a population. • Identify examples of the four levels of data and describe the characteristics of each data type. Not to be used, posted, etc. without my expressed permission. B Heard

  5. You should know the difference between the methods of collecting data. • Sampling (collecting data from part of a population) • Census (collecting data from the entire population – be careful because you can often do this with small groups such as number of vehicles members of the class own, average salary of the class, number of children per house on your street, etc.) • Simulation (Using probabilities to get your results, for example the probability of getting 3 heads in 5 flips of a coin, number of boys out of 5 children, etc.) • Perform an experiment ( often uses things like a control group like researchers giving one group the real medication and the other something that has no effect) Not to be used, posted, etc. without my expressed permission. B Heard

  6. Week 3 Quiz You should be able to identify levels of measurement • Nominal (just a name as in colors, types, number on a jersey, etc.) • Ordinal (Categories that can be ranked meaningfully) • Interval (Distance between values has meaning but there is no “absolute zero” like in the Fahrenheit temperature scale” • Ratio (has an “absolute zero” like the number of children you have, etc. always ask yourself is the lowest possible value zero or none? If so it is probably ratio, if it can go below zero like distance above or below sea level it would be Interval) Chart taken from http://www.socialresearchmethods.net/kb/measlevl.php Not to be used, posted, etc. without my expressed permission. B Heard

  7. Week 3 Quiz Know the difference between inferential and descriptive statistics. • Descriptive statistics are used to reveal patterns through the analysis of numeric data (collect non-numeric data and then analyze). • Descriptive statistics, not surprisingly, "describe" data that have been collected. Commonly used descriptive statistics include frequency counts, ranges (high and low scores or values), means, modes, median scores, and standard deviations. • Inferential statistics are used to draw conclusions and make predictions based on the analysis of numeric data. • Inferential statistics are used to draw conclusions and make predictions based on the descriptions of data. Not to be used, posted, etc. without my expressed permission. B Heard

  8. Week 3 Quiz • Descriptive and Inferential Statistics (additional resources) See the following links: • http://infinity.cos.edu/faculty/woodbury/Stats/Tutorial/Data_Descr_Infer.htm(has some questions and answers) • http://www.habermas.org/stat2f98.htm • http://www.mdx.ac.uk/WWW/STUDY/glonumst.htm Not to be used, posted, etc. without my expressed permission. B Heard

  9. Week 3 Quiz Know the difference between quantitative and qualitative data • Quantitative (numbers with meaning) • Qualitative (Colors, types, etc. and numbers without meaning) Not to be used, posted, etc. without my expressed permission. B Heard

  10. Week 3 Quiz Know the difference in Sampling Techniques • Random (simply picking where every member has an equal chance – drawing out of a bag – generating random numbers) • Stratified (dividing your population into strata and then picking a certain number from each strata) • Systematic (picking every nth one – for example testing every 20th unit off of an assembly line) • Convenience (just asking who is available or who is listening, not making an effort to get a true sample) • Cluster (dividing the population into clusters and sampling everyone in one or two of the clusters) Understand the relationship between a Sample and a Population • A sample is a subset of a population • Sampling is more convenient and easier • Statistics come from Samples • Parameters come from the population (key word “all”) Not to be used, posted, etc. without my expressed permission. B Heard

  11. Week 3 Quiz Some questions…. Not to be used, posted, etc. without my expressed permission. B Heard

  12. Week 3 Quiz A) The following table represents the weights of a number of third graders: Weight Frequency 58-62 2 63-67 3 68-72 5 73-77 7 78-82 11 83-87 10 88-92 4 93-97 2 Total 44 Be Able to: Give the relative frequencies of each class Identify the Class Width Identify the midpoint of the last class Identify the class boundaries Not to be used, posted, etc. without my expressed permission. B Heard

  13. Week 3 Quiz Weight Frequency Relative Freq* Relative Freq(decimal)* 58-62 2 2/44 0.0455 63-67 3 3/44 0.0682 68-72 5 5/44 0.1136 73-77 7 7/44 0.1591 78-82 11 11/44 0.2500 83-87 10 10/44 0.2273 88-92 4 4/44 0.0909 93-97 2 2/44 0.0455 Total 44 Not to be used, posted, etc. without my expressed permission. B Heard

  14. Week 3 Quiz Identify the Class Width Class width is 5 because each class contains five members (first class for example contains 58,59,60,61, and 62) or you can simply the “ending value of the first class “62” from the ending value of the second class “67” (67-62 = 5) Identify the midpoint of the last class 60 because (97+93)/2 = 95 Identify the class boundaries Simply subtract .5 from the lower and add .5 to the upper 57.5-62.5, 62.5-67.5, 67.5-72.5, 72.5-77.5, 77.5-82.5, 82.5-87.5, 87.5-92.5, 92.5-97.5 Not to be used, posted, etc. without my expressed permission. B Heard

  15. Week 3 Quiz The salary data (in thousands) for Bobby Statz’ first 8 years of his career are 25, 28, 32, 36, 41, 48, 51 and 53 Display the data in a stem and leaf plot. Find the mean. Find the median. Find the mode. Find the range. Find the standard deviation. Find Q1, Q2, Q3 Not to be used, posted, etc. without my expressed permission. B Heard

  16. Week 3 Quiz Stem and leaf plot for Bobby Statz’ salary data 2| 58 3| 26 4| 18 5| 13 Not to be used, posted, etc. without my expressed permission. B Heard

  17. Week 3 Quiz Not to be used, posted, etc. without my expressed permission. B Heard

  18. Week 3 Quiz The water level in inches of 10 randomly selected locations in a pond were taken and were as follows: 28, 37, 42, 42, 47, 52, 57, 57, 60, and 62 Display the data in a stem and leaf plot. Find the mean. Find the median. Find the mode. Find the range. Find the range. Find the standard deviation. Find Q1, Q2, Q3 Not to be used, posted, etc. without my expressed permission. B Heard

  19. Week 3 Quiz Stem and leaf plot for water level data 2| 8 3| 7 4| 227 5| 277 6| 02 Not to be used, posted, etc. without my expressed permission. B Heard

  20. Week 3 Quiz Find the mean. 48.5 using average function in Excel Find the median. 50.0 using median function in Excel Find the mode. Bimodal, both 42 and 57 Find the range. Highest value – lowest value = 62-28 = 34 Find the variance. Using sample variance function in Excel (because these were randomly chosen samples) 124.28 (using “VAR” function) Find the standard deviation. Square Root (124.28) = 11.15 (or use “STDEV” function) Find Q1, Q2, Q3 42, 50, 57 respectively using the quartile function in Excel Not to be used, posted, etc. without my expressed permission. B Heard

  21. Week 3 Quiz As an instructor, I have been collecting data to see if I can model a student’s performance on a standardized entrance exam. I determined that the multiple regression equation y = -250+ 16a + 30b, where a is a student’s grade on a quiz, b is the student’s rank on a class list, gives y, the score on a standardized entrance exam. Based on this equation, what would the standardized entrance exam score for a student who makes a 7 on the quiz and had a ranking of 10 be? Not to be used, posted, etc. without my expressed permission. B Heard

  22. Week 3 Quiz y = -250+ 16a + 30b Substitute 7 for “a” and 10 for “b”y = -250+ 16*7 + 30*10y = -250 + 112 + 300y = -250 + 412y = 162 Not to be used, posted, etc. without my expressed permission. B Heard

  23. Week 3 Quiz In my previous example, I determined that the r^2 value (r squared) was .921. What does this tell me? What if my “r” (correlation coefficient) was .654? What would this say? Not to be used, posted, etc. without my expressed permission. B Heard

  24. Week 3 Quiz In my previous example, I determined that the r^2 value (r squared) was .921. What does this tell me? What if my “r” (correlation coefficient) was .654? What would this say? You could say "About 92.1% of the variation in student’s standardized entrance exams can be explained by the score of the quiz and their rank on the class list. The other 7.9% of the variation is either unexplained or is due to other things. As far as the “r” being .654 , I would say that I have a moderately strong positive correlation. Not to be used, posted, etc. without my expressed permission. B Heard

  25. Week 3 Quiz This data shows the Lab Report scores of 8 selected students and the number of hours they spent preparing their Statistics Lab Report. 40 was the highest score the student could make. (hours, scores), (3,34), (2,30), (4,38), (4,40), (2,32), (3,33), (4,37), (5,39) Not to be used, posted, etc. without my expressed permission. B Heard

  26. Week 3 Quiz • Find the equation of the regression line for the given data. • What is the r2 for the data? • What is the r for the data? • What does correlation say about causation? • Predict a Lab Report Score for someone who spent one hour on it. Not to be used, posted, etc. without my expressed permission. B Heard

  27. Week 3 Quiz Predicted score for someone who spent one hour would be: y = 3.158(1) +24.71 y = 27.9 or I would say 28 since all scores are in whole numbers Also, correlation says nothing about causation! Not to be used, posted, etc. without my expressed permission. B Heard

  28. Week 3 Quiz • For the previous set of data find the sum of the x’s, sum of the x’s squared, and sum of the x-squareds. Display your results and label in Excel. Not to be used, posted, etc. without my expressed permission. B Heard

  29. Week 3 Quiz It would be a good idea to be able to discuss how these relate to the correlation coefficient (see formula). Not to be used, posted, etc. without my expressed permission. B Heard

  30. Week 3 Quiz Stronger Negative Correlation Stronger Positive Correlation -1 0 +1 “r” Not to be used, posted, etc. without my expressed permission. B Heard

  31. Week 3 Quiz S STAT CAVE See you next week: “Same Stat Time, Same Stat Channel” Not to be used, posted, etc. without my expressed permission. B Heard

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