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Integrating the Computer and the Calculator in the Statistics Classroom International Conference on Technology in Collegiate Mathematics Friday, November 5, 1999 Session: S11 Location: Boardroom IV 8:00 -8:45 AM San Francisco 11/1/99 [email protected] 2# Integrating the Computer and the Calculator in the Statistics Classroom Roseanne Hofmann Montgomery County Community College [email protected] Special Thanks to: MCCC Foundation Dean Brad Gottfried Shayne Clark Wallis Students who used the materials 11/1/99 [email protected] 4# Talking isn’t 11/1/99 [email protected] T e a c h i n g 5# Listening isn’t Learning 11/1/99 [email protected] 6# Research encourages teachers to Use a Constructivist Approach in Teaching. Give up the role of “sage on the stage” to become “guide on the side.” 11/1/99 [email protected] 7# Changes in Teaching Focus Student Centered Teacher Centered 11/1/99 [email protected] 8# Give a fish and they eat for a day; teach them to fish and they eat for a lifetime. 11/1/99 [email protected] 9# “Lure” students into Mathematics by getting them to “play” with interesting application problems. 11/1/99 [email protected] 10# Visualization in the broadest sense has always been important in mathematics. Teaching based on visualization requires us to relearn many of our pedagogical skills. 11/1/99 [email protected] 11# Dock and Teach Borrowing a term from the business world that uses portable computers Purpose of Internal Grant • Use of Notebook Computer in Classroom, Office, and Home • Writing of Multimedia modules for Elementary Algebra 11/1/99 [email protected] 13# Bonus •Use computer for PowerPoint presentations supplied by Statistics textbook •Use computer for Statistics CD authored by Velleman 11/1/99 [email protected] 14# Hardware - Obvious • Projector • Portable Computer • Connection to Network • TI-83 Plus Calculator 11/1/99 [email protected] 15# Software • Velleman CD disk • Triola PowerPoint Slides 11/1/99 [email protected] 16# Cost Concerns • Software • Textbook • Calculator 11/1/99 [email protected] 17# Teaching • Balance of PowerPoint and Velleman CD • Graphics Calculator • Group Learning • Simulations in Class 11/1/99 [email protected] 18# MONTGOMERY COUNTY COMMUNITY COLLEGE Introduction to Statistics I Fall, 1999 MAT 131 BC 9:05-10:00 a.m. PH Room 116 MAT 131 CC 10:10-11:05 A.M. PH Room 116 Roseanne Hofmann, Ed.D. [email protected] CATALOG DESCRIPTION A basic course designed for students in all fields. Topics include organization of data, measures of central tendency, measures of variation, statistical inference and correlation. This is a self-contained course. With MAT 132, it is a course with greater depth and applications. A graphing calculator is required for class, homework, and testing. Classroom instruction and programs will be presented using a TI-83+ graphing calculator. PREREQUISITES Math placement test recommendation of “ABV 100” (above MAT 100) or MAT 100, with a minimum grade of “C”. 11/1/99 [email protected] 19# OBJECTIVES/OUTCOMES Upon completion of this course, students should be able to 1. Understand descriptive statistics by being able to find by hand and using the TI calculator, mean, median, mode, midrange, range, variance and standard deviation for a given set of data. 2. Make frequency tables, histograms, frequency polygrams, ogives, pie charts, stem and leaf plots and box plots. 3. Solve probability problems using the addition and multiplication rules and complementary events. 4. Understand probability distribution, random variable, mean, variance, and expectation for the binomial and normal distributions. 5. Understand the normal distribution as an approximation to the binomial distribution and the Central Limit Theorem. 6. Estimate sample sizes of means and sample sizes of proportions. 7. Test hypotheses: test a claim about a mean, understand p-values, a t-test, and tests of proportions. 8. Make inferences from two samples using means and proportions. 9. Understand correlation and regression. 10. Understand multinomial experiments and contingency tables. 11. Use the TI graphing calculator to do many of the statistical tests described above. 11/1/99 [email protected] 20# REQUIRED MATERIALS Required Text: Elementary Statistics, 7th edition, Mario F. Triola, Addison-Wesley Publishing Company, 1998. 1. A TI-83+ graphing calculator 2. ActivStats, CD-ROM, Paul Velleman SUGGESTED TEXTBOOKS 1. Student’s Solution Manual to accompany the textbook, Milton Loyer 2. TI-83 Companion to Elementary Statistics, 7th edition, Larry Morgan Student projects will be required. 11/1/99 [email protected] 21# TENTATIVE SCHEDULE September 1 1.1, 1.2; V3.1 3 1.3, 1.4; V8.1 8 2.1, 2.2; V3.2 10 2.3; V4.1 October November 13 2.4; V4.2 15 2.5; V5.1 17 2.6 October 11/1/99 20 22 24 27 29 1 2.7; V2.7 Review Test 1 Chs. 1 and 2 3.1, 3.2 Project Due; V10.1 3.3 3.4; V9.1, 11.1 4 6 8 11 13 15 4.1, 4.2; V13.1 4.3 4.4 Review Test 2 Chs. 3 and 4 5.1, 5.2; V12.1 18 5.3, 5.4; V14.1 20 5.5 22 5.5 25 7.1, 7.2; V17.1 27 7.3 29 7.3 1 7.4 3 7.5; V19.1 5 Review 8 Test 3 Chs. 5 and 7 10 6.1, 6.2; V15.1 12 6.3; V16.1 15 6.4; V19.1 17 9.1, 9.2; V21.1 19 9.3; V22.1, 23.1 22 10.1, 10.2 Project Due; V24.1 December [email protected] 29 10.3 1 8.1, 8.2; V20.1 3 8.3, 8.4 6 8 10 13 Review Test 4 Chs. 6, 9, 10, 8 Review Last Class 22# First Day Data Sheet Data Sheet 1. _______Sex 2. _______Married/Single 3. _______Height(In) 4. _______Number of Brother and Sisters 5. _______Number of Children 6. _______Birth Month 7. _______Number of Credits currently enrolled for 8. _______Average Number of hours of Sleep per night 9. _______Number of Pierced Ears 10. _______Watch Soaps regularly – yes/no 11. _______Pulse Rate 12. _______Amount of change in pocket or purse 11/1/99 [email protected] 23# MAT 131 Fall 1999 Statistics Project (50 points) PART I Due date: Monday, September 27, 1999 Remember neatness counts and there is a grade reduction for lateness. 1. (10 pts.) Randomly survey 32 people over 18 years of age. Use either all males or all females. Obtain the following data for each: a. their hand size, measured to the nearest 1/4 inch b. their shoe size, to the nearest 1/2 inch (Do not include width.) List the data in the pairs obtained: i.e. person 1 hand size shoe size person 2 hand size shoe size 2. (5 pts.) State a purpose for this project. This means you must invent a reason for wanting the required data. (Use your imagination.) Also state a specific population. (Think about who your sample represents.) 3. (18 pts.) For the hand size data: find: MEAN, MEDIAN, MODE, RANGE, VARIANCE, STANDARD DEVIATION, Q1, Q3. Show any work or explain what you did to get your answers. ALSO, explain what information Q1 gives you in terms of your numbers. 4. (6 pts.) Arrange the hand size data into grouped data. Use 4 or 5 classes. Find: MEAN, MEDIAN, VARIANCE, STANDARD DEVIATION for this grouped data. Explain what you did or show how you got your answers. 5. (5 pts.) Compare the common parts of question #3 and #4. What do you conclude? 6. (6 pts.) Arrange the show sizes into a frequency distribution (grouped data) and again use 4 or 5 groups. Make a histogram for this grouped data, carefully labeling each axis with numbers and names. The histogram should also have a title. 11/1/99 [email protected] 24# PART II Due date: Monday, November 22, 1999 For Part II of the project, use the raw data, not the grouped data. Attach a copy of your original data. Then summarize your data in a table like the following: HAND SIZE SHOE SIZE Sample mean, x Sample standard deviation, s Sample size, n You must show all work (not just answers). If you use your calculator to find an answer, explain carefully what you did. Again, neatness counts and there is a grade reduction for lateness. 7. (18 pts.) For the HAND SIZE data: a. Give the best point estimate for the average hand size based on your sample results; b. Depending on whether your sample was composed of males or females, test the claim that: AVERAGE HAND SIZE FOR MEN IS 7 1/2 AVERAGE HAND SIZE FOR WOMEN IS 6 1/2 In either case, assume that the population is normally distributed and state your conclusion for = 0.05. Give the P-value for the test. c. Determine a 98% confidence interval for . Again, assume the population is normally distributed. 8. (8 pts.) For the SHOE SIZE data: a. Determine the best point estimate for the proportion of women with shoe size 6 or of men with shoe size 9, depending on your sample; b. Determine a 99% confidence interval for this point estimate. 9. (6 pts.) Referring back to the paired data (#1), draw a scatter diagram. Label each axis carefully with names and numbers. Your scatter diagram should have a title. 10. 11. 12. (8 pts.) Find "r," explaining how you did it. Determine if there is a linear correlation between shoe sizes and hand sizes. ( = 0.05) (8 pts.) Regardless of your answer to the previous question, determine the equation for the regression line and graph the line on the scatter diagram done in #10. Be sure to give the points you used to graph the line. (2 pts.) Use the regression line found in #11 to predict the shoe size of a person whose hand size is 6 1/4". 11/1/99 [email protected] 25# Mat 131 Jigsaw Grouping Tool 1. Complete collection of elements to be studied 2. A subset of a population 3. Numerical measurement describing some characteristic of a population 4. Numerical measurement describing some characteristic of a sample 5. Zip code - level of measurement 6. Cars described as subcompact, compact, intermediate - level of measurement 7. Temperatures of irate Mat 131 students over price of book - level of measurement 11/1/99 [email protected] Population Sample Parameter Statistic Nominal Ordinal Interval 26# Grouping Tool 8. Annual income of doctors - level of measurement 9. Number of Siblings - discrete or continuous 10. Heights of Students - discrete or continuous 11. Equal chance of being selected numbers in hat 12. A sociologist at the CC College surveys all students from each of 20 randomly selected 4 English Classes 13. A sociologist at the CC College selects 12 men and 12 women from each of 4 English classes 11/1/99 [email protected] Ratio Discrete Continuous Random sample Cluster Stratified sample 27# DATA SETS Given the following data sets find the mean, mode, median, and standard deviation. Make a table with the data sets in rows and the mean, mode median, and standard deviation in columns. Draw a box plot and a histogram for each. A = 2,3,4,5,6,14,15,16,17,18 B = 2,10,10,10,10,10,10,10,10,18 C= 2,2,2,2,3,16,18,18,18,18 D = 2,3,5,5,6,10,15,18,18,18 E = 2,4,10,10,10,10,10,10,16,18 F = 2,4,8,9,10,10,12,16,18 G = 8,9,9,9,10,10,10,10,11,11,12,13 H = 52,53,55,55,56,60,65,68,68,68 J = 8,8,9,9,9,11,11,11,11,11 11/1/99 [email protected] 28# Input the data in L1, L2, L3, etc. Share the list with your partner by having your partner use GetCalc from the catalogue. Then use One Variable statistics on each list. 11/1/99 [email protected] 29# Source:http://m-ms.com/factory/history/faq1.html 11/1/99 [email protected] Hofmann 30# MAT 131 Multiple Choice Test Name ____________________________________________ 1. The period of time during which reptiles first appeared on earth is the _____ period. a. Jurassic d. Cambrian b. Devonian e. Lower Cretaceous c. Triassic 2. The King of England from 1820 to 1830 was a. George I b. George II c. George III d. George IV e. George V 3. The chemical element with the atomic number 77 is a. Iridium d. Thallium b. Osmium e. Rhodium c. Rhenium 4. a. b. c. The King of Spain from 1452 to 1516 was Ferdinand I Ferdinand II Ferdinand III d. Ferdinand IV e. Ferdinand V 5. The Babylonian cuneiform numeral for 131 is a. 9 I b. c. C X X X I d. e. 11/1/99 [email protected] 31# 6. The third largest planet in our solar system is a. Saturn d. Uranus b. Earth e. Neptune c. Jupiter 7. The 11th president of the United States was a. Fillmore d. Tyler b. Polk e. Buchanan c. Pierce 8. The first two men on the moon were Armstrong and Aldrin. On that Apollo flight, who was the third crew member? a. Shepard d. White b. Schirra e. Collins c. Grissom 9. Who recorded the 1979 disco hit “Bad Girls?” a. Patti LaBelle d. Gladys Knight b. Robert Flack e. none of the above c. Donna Summers 10. The real name of Lewis Carroll is a. Charles Lamb d. Charles Dodgson b. Charles Brown e. Charles McCarthy c. Charles Doyle 11/1/99 [email protected] 32# 11/1/99 [email protected] 33# Triola, page 258: Given that the population of men has normally distributed weights, with a mean of 173 lb. and a standard deviation of 30 lb., find the probability that if one man is randomly selected, his weight is greater than 180 lb. 11/1/99 [email protected] 34# Triola, page 362 The Jack Wilson Health Club claims in advertisements that “you will lose weight after two days of the Jack Wilson diet and exercise program.” The Dade County Bureau of Consumer Affairs conducts a test of that claim by randomly selecting 33 people who have signed up for the program. It was found that the 33 people lost an average of .37 lb., with a standard deviation of .98 lb. Use a .05 level of significance to test the advertised claim. 11/1/99 [email protected] 35# 11/1/99 [email protected] 36# Important Distributions Normal Uniform 11/1/99 Skewed Right [email protected] Skewed Left 37# Notation S denotes the summation of a set of values x is the variable usually used to represent the individual data values n represents the number of data values in a sample N represents the number of data values in a population x is pronounced ‘x-bar’ and denotes the mean of a set of sample values µ is pronounced ‘mu’ and denotes the mean of in a population all values 11/1/99 [email protected] 38# Definitions Mean the value obtained by adding the scores and dividing the total by the number of scores S x Sample x = n Population 11/1/99 Sx µ = N [email protected] 39# Definition Standard Normal Distribution • a normal probability distribution that has a • mean of 0 and a standard deviation of 1 •Area found in •Table A-2 •Area = 0.3413 •0.4429 -3 -2 11/1/99 -1 0 1 Score (z ) Figure 5-5 2 3 [email protected] 0 z = 1.58 Figure 5-6 40# Figure 5-10 "greater than x" "at least x" "more than x" "not less than x" Interpreting Area Correctly Add to 0. 5 Subtract from 0. 5 0. 5 x "less than x" "at most x" "no more than x" "not greater than x" x Subtract from 0.5 Add to 0. 5 0.5 x x Add C Use A=C–B A B "between x1 and x2 " 11/1/99 x1 x 2 [email protected] x1 x 2 41# 7-1 Overview Definition Hypothesis in statistics, is a claim or statement about a property of a population Method of Reasoning Analyze a sample in an attempt to distinguish between results that can easily occur and results that are highly unlikely. 11/1/99 [email protected] 42# 11/1/99 [email protected] 43# 11/1/99 [email protected] 44# 11/1/99 [email protected] 45# 11/1/99 [email protected] 46# 11/1/99 [email protected] 47# 11/1/99 [email protected] 48# Assessment 11/1/99 [email protected] 49# Mat 131 Students Survey – Velleman CD During this semester, I have asked you to use the Velleman CD. Sometimes I have used Velleman to demonstrate different topics being discussed in class. Please give your candid opinion about this CD. 1. Is the Velleman CD helpful? Explain: 2. Were parts of Velleman(movies, testing, etc.) more helpful than others? Which? Why? 3. Should I use Velleman next semester? Explain: 4. If this course were given on-line (no face-to-face instruction – strictly computer) would you recommend that the students purchase the Velleman CD? 5. Were the powerpoint slides helpful? Explain: 6. Were the powerpoint handouts helpful? Explain: 11/1/99 [email protected] 50# RESULTS Mat 131 Students Survey – Velleman CD 1. Is the Velleman CD helpful? Explain: Yes 12 So-So 5 No 9 2. Were parts of Velleman(movies, testing, etc.) more helpful than others? Which? Why? 3. Should I use Velleman next semester? Explain: Yes 17 Optional 2 No 9 4. If this course were given on-line (no face-to-face instruction – strictly computer) would you recommend that the students purchase the Velleman CD? Yes 23 No 2 5. Were the powerpoint slides helpful? Explain: Yes 19 So-So 3 No 4 6. Were the powerpoint handouts helpful? Explain: 11/1/99 [email protected] 51# 11/1/99 [email protected] 52# Velleman CD 11/1/99 [email protected] 53# Would I do it again? Yes, for the students. • Computer animations surpass chalk and talk • Sound helped ESL students • CD allows students to review • Access for students who missed class 11/1/99 [email protected] 54# Would I do it again? Yes, for the teacher. Would I recommend that you try it? Yes! • Immediacy • Flexibility on two levels • Computer Animations • Visualization • Record of material presented • Computer is another teaching tool 11/1/99 [email protected] 55# Q uestions 11/1/99 [email protected] 56#