Video Aided Instruction, Inc.Roslyn Heights, New York1This study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.StatisticsStudy GuidebyDavid M. Levine, Ph.D.#VAI-S1787v1.1To inquire about any of our products:web:videoaidedinstruction.come-mail:custsvc@videoaidedinstruction.comphone:1-800-238-1512 or 516-939-0707fax:516-935-5552mail:Video Aided Instruction, Inc.P.O. Box 332Roslyn Heights, NY 11577-03322This study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Algebra 2& Trigonometryset of 5 DVDsThis study guide should be used along with the follow-ing program published by Video Aided Instruction. The instructor works through the exercises found in this guide and much, much more during the course of the actual program.Statistics3 DVDs 6 hrs.item #VAI-1787price $119.95isbn 1-57385-178-7upc 600459178796Copyright 2007 Video Aided Instruction, Inc.To all users of the Video Aided Instruction publication named above, permission is hereby granted to create one (1) paper imprint of this document per person. In addition, teachers and librarians may reproduce paper imprints of this document in quantities not to exceed one hundred (100) imprints annually. All imprints and reproductions made must retain all copyright notices contained herein. This authorization is granted for this specific document only, and only when the document is used along with the publication named above.Any reproduction or distribution of this electronicdocument file itself for example, copying this file to orfrom an Internet server, a disc, or an e-mail message isstrictly prohibited. In addition, no part of this document may be reproduced by any means or for any purpose other than as an aid during self-study or group instruc-tion along with the aforementioned publication.Other Video Aided Instruction titles you might enjoy:Probabilityset of 2 DVDsStatistics Study GuideIntroductionStatistics isnt just for math majors: now its taught in high school, and its even a required course for many college degrees in psychology, sociology, business, economics, engineering, and other fields. Now every student can master this course quickly and easily!The ultimate resource for AP high school students, college students, and adult learners, this set coversthe standard topics taught in introductory stats classes and is jam-packed with practice questions and strategies for tackling even the most complicated problems.For easier studying and maximum success, we recom-mend that you view the program over a number of short sessions: dont try to absorb too much at one time. Review the entire program, or specific sections, as many times as you find necessary in order to mas-ter the material.Remember, you control the pace of your own learn-ing with Video Aided Instruction. While watching this program, you can use the following buttons on your remote control or DVD player:UseREVERSE SKIPto start overthe problem or section that youre watching.UseFORWARD SKIPto jump aheadto the next problem or section.UsePAUSEto temporarily freeze the screen so you can read important graphicsor try to answer questions on your own.Also, be sure to keep plenty of scrap paper handy so you can jot down ideas, work through concepts, and more. Finally, be sure to use the myriad on-screen graphics to take notes for yourself when youre done, youll have a notebook you can refer back to again and again.Now its easier than ever to earn high test marks in school or relearn forgotten mathematics all with your own private teacher!About Your InstructorDavid M. Levine, Ph.D., is a Professor Emeritus of Sta-tistics and Computer Information Systems at Baruch College, City University of New York. Dr. Levine is an award-winning educator and bestselling author. He has written 14 textbooks, many of which have been translated into foreign languages and adopted by leading academic institutions around the world.Statistics Study Guide3Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.PART 1 DefinitionsFor each of the following variables, indicate whether the variable is quantitative or qualitative. If the vari-able is quantitative, indicate whether it is discrete or continuous.1.Ownership of a CD player.2.The number of albums and discs purchased in the last year.3.The playing length of the last album or disc purchased.4.Favorite type of music.PART 2 Review of Summation Notation1.Given the following:X Y3 54 16 23 71 0Compute:(a) Xi(b) Yi(c) Xi2(d) Yi2(e) X Yi i2.Given the following:X Y3 25 61 44 27 3Compute:(a) Xi(b) Xi2(c) X Yi i(d) X Yi i( ) (e) cX ci,where= 2(f) Xi ( )44Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study GuidePART 3 Descriptive Statistics1.The following data represent the pulse rates (in beats per minute) of a sample of incoming fresh-men at the time of their medical examinations:49, 74, 66, 68, 78, 53, 57, 62, 61, 66In (a)(k), compute:(a)arithmetic mean(b)median(c)mode(d)first quartile (Q1) (e)third quartile (Q3)(f)range(g)variance(h)standard deviation (i)coefficient of variation(j)midrange(k)midhinge(l)Based on the results in (a)(k), indicate whether the distribution is right-skewed, symmetric,or left-skewed.(m)Set up a box-and-whisker plot for these data.2.The following data represent the cost of a lunch time Deluxe Hamburger Special, consisting of a hamburger, french fries, and regular soft drink at a sample of 15 coffee shops within a 10-block radius of a large urban college.Coffee Shop Cost ($) Coffee Shop Cost ($)A 4.75 I 4.60B 4.30 J 4.85C 4.05 K 4.75D 4.55 L 4.55E 4.60 M 4.90F 3.90 N 4.55G 5.25 O 4.95H 4.65Compute:(a)arithmetic mean(b)variance (c)standard deviation (d)coefficient of variation(e)median(f)mode(g)first quartile (Q1) (h)third quartile (Q3)(i)range(j)midrange(k)midhinge5Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide3.The commuting time of a population of employees of a large company has a population mean of 45 minutes and a population standard deviation of 8 minutes.(a)At least 75% of the employees will have commuting times between what two values?(b)At least what percentage of the employees will have commuting times between33 and 57 minutes? ERRATUM NOTICE In the very last step of the solution for Part 3, question 3, part (b), the writing on the chalkboard in the video includesa typographical error which causes the instructor to misstate the correct answer to this question. The calculation of theexpression111 52( . ) should have yielded ~.5556 (not ~.8889 as written on the chalkboard). Thus, the correct answer should have been stated as approximately 55.56%. We sincerely apologize for any confusion that this error may cause.PART 4 Data Presentation: Tables & Charts1.The following data represent the grade point averages (GPAs) of a sample of 50 freshmen at the end of their first year of study.GPAs of 50 Freshmen1.95 3.42 3.97 3.56 2.94 2.04 3.07 3.94 2.54 1.643.14 3.77 1.80 2.32 3.44 2.21 2.96 3.98 2.59 3.302.82 2.98 3.99 3.50 2.46 2.87 3.35 2.18 3.33 1.933.45 3.26 3.00 3.09 2.60 2.86 3.72 3.32 2.77 2.952.15 2.38 3.66 3.02 2.28 2.70 3.85 2.75 2.59 3.15(a)Construct a frequency distribution of the GPA values using 1.6 to under 2.0 as the first class,2.0 to under 2.4 as the second class, , and 3.6 to under 4.0 as the last class.(b)Form the relative frequency distribution.(c)Form the percentage distribution.(d)Form the cumulative percentage distribution.(e)Plot the histogram.(f)Plot a percentage polygon.(g)Plot the cumulative percentage polygon (ogive).6Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide2.The following data represent the interest rate (in percentage points of interest per year) provided by 6-month certificates of deposit at a sample of 200 savings banks in a particular state.Interest Rate Frequency5.5 under 6.0 396.0 under 6.5 566.5 under 7.0 477.0 under 7.5 337.5 under 8.0 158.0 under 8.5 10Total: 200(a)Approximate the arithmetic mean of this frequency distribution.(b)Approximate the standard deviation of this frequency distribution.(c)Form the percentage distribution.(d)Form the cumulative percentage distribution.(e)Plot the histogram.(f)Plot a percentage polygon.(g)Plot the cumulative percentage polygon (ogive).3.A sample of 50 students was asked to indicate their preference for various types of soft drinks. The results were as follows:Soft Drink FrequencyCola 27Lemon-Lime 9Orange 5Root Beer 3Other 6Total: 50(a)Compute the percentage preferring each type of soft drink.(b)Construct a bar chart.(c)Construct a pie chart.7Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study GuidePART 5 Normal Distribution & Sampling Distribution of the Mean1.Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1):(a)What is the probability that Z is between 0 and 1.24?(b)What is the probability that Z is less than 1.24?(c)What is the probability that Z is greater than 1.73?(d)What is the probability that Z is between 1.24 and 1.73?(e)What is the probability that Z is less than 1.24 or greater than 1.73?(f)What is the probability that Z is between 1.24 and 1.24?(g)What is the probability that Z is less than 1.24 or greater than 1.73?(h)What is the value of Z if 67.36% of all the values are larger?(i)What is the value of Z if 2.5% of all the values are larger?(j)Between what two values of Z (symmetrically distributed around the mean) will 76.2%of all the values be contained?2.The amount of tea used daily at a local Chinese restaurant is normally distributed with a mean of 8500 ounces and a standard deviation of 800 ounces.(a)What is the probability that on a randomly selected day the amount used will be between 8500 and 9100 ounces?(b)What is the probability that on a randomly selected day the amount used will be more than9100 ounces?(c)What is the probability that on a randomly selected day the amount used will be between6500 and 7500 ounces?(d)What is the probability that on a randomly selected day the amount used will be less than6500 ounces or more than 7500 ounces?(e)On 85% of the days, the amount of tea used will be more than how many ounces?3.A multiple choice test is given in which there are 4 possible answers for each of 25 questions. Sup-pose that a student is not familiar with the test material and has decided to randomly guess the answer to each question (there is no penalty for incorrect guesses). In the absence of any other information, the student assumes that each of the 4 possible answers is equally likely to occur.(a)On the average, how many questions would you expect the student to answer correctlyout of the 25 questions?(b)What is the approximate probability that the student will answer exactly 10 questionscorrectly?(c)What is the approximate probability that the student will answer at least 10 questionscorrectly?(d)What is the approximate probability that the student will answer between 5 and 8 questions(inclusive) correctly?8Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide4.The amount of tea used daily at a local Chinese restaurant is normally distributed with a mean of 8500 ounces and a standard deviation of 800 ounces. If a random sample of 64 days is selected:(a)what is the probability that the sample mean will exceed 8673 ounces?(b)what is the probability that the sample mean will be between 8300 and 8700 ounces?(c)between what two values (symmetrically distributed around the population mean) will92.98% of the sample means be contained?5.Suppose that the cholesterol level of ten-year-old girls is normally distributed with a mean of 175 and a standard deviation of 20. A sample of 25 ten-year-old girls is selected.(a)What is the probability that the sample mean cholesterol level will be above 185?(b)Between what two values (symmetrically distributed around the population mean) will 95% ofall the sample means be contained?PART 6 Confidence Intervals & Sample Size Determination1.Suppose that the scores on a certain IQ test are known to be normally distributed with a popula-tion standard deviation of 15. If a sample of 25 scores indicates a sample mean of 106, set up a 95% confidence interval estimate of the population average IQ score.2.The following data represent the pulse rates (in beats per minute) of a sample of incoming fresh-men at the time of their medical examinations:49, 74, 66, 68, 78, 53, 57, 62, 61, 66Set up a 95% confidence interval estimate of the population average pulse rate of incomingfreshmen.3.The management of a car dealership conducted a telephone survey to determine the proportion of customers who were satisfied with services performed on their cars in the past month. A random sample of 100 customers indicated that 59 reported that they were satisfied. Set up a 90% confi-dence interval estimate of the population proportion of customers who were satisfied with their service.4.A random sample of 75 children was interviewed upon leaving an aquarium; 45 reported that the seals were their favorite aquatic creature. Set up a 99% confidence interval estimate of the popula-tion proportion of children visiting the aquarium who prefer the seals.5.The Board of Trustees of the Scholarship Fund of a local high school would like to estimate the con-tributions that can be expected from past contributors in the upcoming year. The chairperson of the committee would like to have 95% confidence of estimating the true average amount donated to within $5. Based on last years contributions, the standard deviation is estimated as $17. What sample size should be selected?9Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide6.A researcher for a public interest group would like to estimate the proportion of adults over the age of 18 in a particular community who are not registered to vote. She wishes to have 95%confidence of being correct to within .06 of the true population proportion. Previous surveys in other communities have indicated a proportion of .35. What sample size should be selected?7.The Market Research Director for a large department store would like to study mens spending per year on dress shirts.(a)A survey is to be sent to a sample of the stores credit card holders to determine the averageyearly amount that men spend on dress shirts. If the market researcher wanted to have 99%confidence of estimating the true average to within $10 and the standard deviation isassumed to be $28 (based on previous studies), what sample size is needed?(b)A survey is to be sent to a sample of the stores credit card holders to determine thepopulation proportion of men whose dress shirts are primarily purchased by themselves. If themarket researcher wishes to have 90% confidence of estimating the true proportion to within .04, what sample size is needed?(c)Suppose the department store has 2,000 credit card holders. What would be your answer inpart (a)?(d)Suppose the department store has 2,000 credit card holders. What would be your answer inpart (b)?8.Suppose that in problem 3 of this part, there was a population of 800 customers. Recalculate the confidence interval developed there.PART 7 One-Sample Tests of Hypothesis1.Suppose that scores on a certain aptitude test were known to have a population mean of100 and a population standard deviation of 10. A new version of the test is to be given to a sample of 50 students who have been carefully selected to represent a cross-section of the population of students who would be taking the test. The average score of this sample test was 101.1. Assuming that the population standard deviation had not changed from the previous test, at the .05 levelof significance, is there any evidence that the average score on the new test would be different from 100?2.The following data represent the pulse rates (in beats per minute) of a sample of incoming fresh-men at the time of their medical examinations:49, 74, 66, 68, 78, 53, 57, 62, 61, 66At the .01 level of significance, is there evidence that the average pulse rate of incoming freshmen is different from 50 beats per minute?3.An investigator for a State Highway Department needed to test the speed of cars on a particular section of an interstate highway in order to qualify for federal highway funds. Suppose that a sample of 30 cars taken at a particular point on the highway revealed a sample average speed of 61.3 miles per hour with a sample standard deviation of 9.7 miles per hour. At the .05 level of sig-nificance, is there evidence that the population average speed is greater than 55 miles per hour?10Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide4.An admissions officer of a college wanted to determine whether the proportion of entering fresh-men who indicated a desire to major in Business had changed in the past year. A random sample of 200 of this years freshmen indicated that 77 expressed a desire to major in Business. At the .01 level of significance, is there evidence of a change from last year in which the population propor-tion was .40?5.The Home Mortgage Department of a bank has just instituted a new system to streamline the pro-cess of a decision concerning the approval of a home mortgage equity loan. Under the old system, 75% of the applications had final decisions made within 30 days. A random sample of 100 applica-tions processed under the new system revealed that 87 had decisions made within 30 days. At the .05 level of significance, is there evidence that the proportion of applications in which decisions are made within 30 days has increased under the new system?6.Find the p-value in problem 1 of this part, and use the p-value approach to reject or to not reject the null hypothesis.7.Find the p-value in problem 5 of this part, and use the p-value approach to reject or to not reject the null hypothesis.PART 8 Testing Differences Between the Means of Two Groups1.Suppose that we wanted to study sales of annual plants at two branches of a large garden supply chain. Samples of customers were selected with the following results:Branch A Branch BX11.73 9.94S 6.32 5.14n 42 26At the .05 level of significance, is there evidence of a difference in the average sales betweenBranch A and Branch B?11Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide2.A pharmaceutical company wanted to determine the effectiveness of a new drug in lowering the cholesterol level of patients with current levels of at least 200. A clinical trial of the new drug was conducted on a sample of 12 patients with the following results:Cholesterol LevelsPatient Before After1 236 2212 257 2483 204 2054 229 1985 288 2696 253 2307 235 2188 275 2499 240 22710 216 20711 226 21912 264 252At the .01 level of significance, is there evidence that the average cholesterol level is higherbefore the medication was taken that at the conclusion of the clinical trial?3.A career guidance counselor at a large university wanted to study the scores on the mathematics section of a standard aptitude test for Liberal Arts and for Business majors. A sample of 25 students from each type of major was selected with the following results:MajorLiberal Arts BusinessX473.6 521.8S 138.1 125.9n 25 25At the .01 level of significance, is there evidence that the average mathematics score is lowerfor Liberal Arts majors than for Business majors?12Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide4.The Research Director for a company that develops video games wanted to determine which one of two video games should have marketing priority. An experiment was devised in which 10 young-sters ranging in age from eight to fifteen years were allowed to play each game on a particular video game system for a particular period of time. After playing each game (the order of which game was played first was randomized for each child), the child indicated the amount of money (in dollars) that he or she would be willing to pay for the game. The results were as follows:GameChild A B1 21 342 29 223 23 294 35 435 19 256 25 257 29 398 23 219 27 3210 18 20At the .05 level of significance, is there any evidence of a difference in the average price that wouldbe paid for the two video games?PART 9 Testing for Proportions & Chi-Square Tests1.The owner of a car dealership conducted a survey to determine whether there was a gender differ-ence in ones satisfaction with the service received. A sample of 100 women showed that 65 were satisfied, while a sample of 100 men showed that 80 were satisfied. At the .01 level of significance, is there any evidence of a difference in satisfaction with service between men and women?2.Do problem 1 of this part using the chi-square test.13Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide3.A poll was taken concerning attitudes of voters toward the institution of a common poll closing time on Election Day during presidential election years. The results, categorized according toregions of the United States, were as follows:RegionFavor East South Midwest West TotalYes 215 125 146 92 578No 185 75 54 108 422Total 400 200 200 200 1000At the .05 level of significance, is there evidence of a difference in attitude between the various regions of the United States?PART 10 Regression & Correlation1.A garment manufacturer was interested in predicting the annual maintenance cost of sewing ma-chines based upon the age of the machine. A sample of 16 machines revealed the following ages and maintenance costs in the last year:MachineXAge (Years)YCost ($) MachineXAge (Years)YCost ($)1 8 109 9 1 252 3 75 10 3 703 1 21 11 6 1264 9 135 12 2 585 5 67 13 1 306 7 125 14 2 477 5 71 15 6 1208 2 52 16 8 105(a)Compute the regression coefficients the Y-intercept (b0), and the slope (b1) in thisproblem.(b)Predict the average maintenance cost for a machine that is four years old.(c)Compute the coefficient of determination (r2) and interpret its meaning in this problem.(d)Compute the coefficient of correlation r.(e)Compute the standard error of the estimate.(f)At the .05 level of significance, is there evidence of a linear relationship between ageand maintenance cost?14Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide2.The following data represent the heights in inches of a sample of 10 husbands and their wives:Heights of Married Couples (Inches)Husband 68 69 73 70 67 74 72 75 67 72Wife 64 62 56 67 66 69 66 71 64 60(a)Compute the coefficient of correlation r.(b)At the .05 level of significance, is there evidence of a relationship between the heightof husbands and the height of wives?PART 11 Analysis of Variance1.At one time, the Director of Consumer Affairs of a large suburban county wanted to study whether there were any differences in the price of unleaded regular (87 octane) gasoline for four major brands of gasoline sold in the county. A random sample of five service stations was selected for each of the four brands and the price (in cents) on a particular day was recorded with thefollowing results:Prices of Gasoline Brands (Cents)A B C D111.9 116.3 112.8 109.9114.9 117.4 113.5 109.5116.5 118.4 116.8 110.9115.8 113.6 115.4 111.3118.4 116.4 114.8 112.5At the .05 level of significance, is there evidence of a difference in the average price between the different brands?15Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide2.An agronomist was interested in measuring the differences in the yield of three types of string beans. Five plants of each type of string bean were planted with the following results (yield in pounds):TypeA B C42 46 5257 52 4759 56 5847 50 4649 51(Note that one plant of type B was accidentally destroyed soon after being planted.)At the .01 level of significance, is there evidence of a difference in the average yield of the three types of string beans?16Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study GuideTABLE 1 The Standardized Normal DistributionIn this program, Dr. Levine uses a table of the Standardized Normal Distribution like that shown below. Each entry in this table represents the area under the standardizednormal distribution from the mean to Z.Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .090.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .03590.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .07530.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .11410.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .15170.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .18790.5 .1915 .1950 .1985 . 2019 . 2054 . 2088 . 2123 . 2157 . 2190 . 22240.6 . 2257 . 2291 . 2324 . 2357 . 2389 . 2422 . 2454 . 2486 . 2518 . 25490.7 . 2580 . 2612 . 2642 . 2673 . 2704 . 2734 . 2764 . 2794 . 2823 . 28520.8 . 2881 . 2910 . 2939 . 2967 . 2995 .3023 .3051 .3078 .3106 .31330.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .33891.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .36211.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .38301.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .40151.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .41771.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .43191.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .44411.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .45451.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .46331.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .47061.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .47672.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .48172.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .48572.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .48902.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .49162.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .49362.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .49522.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .49642.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .49742.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .49812.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .49863.0 .49865 .49869 .49874 .49878 .49882 .49886 .49889 .49893 .49897 .499003.1 .49903 .49906 .49910 .49913 .49916 .49918 .49921 .49924 .49926 .499293.2 .49931 .49934 .49936 .49938 .49940 .49942 .49944 .49946 .49948 .499503.3 .49952 .49953 .49955 .49957 .49958 .49960 .49961 .49962 .49964 .499653.4 .49966 .49968 .49969 .49970 .49971 .49972 .49973 .49974 .49975 .499763.5 .49977 .49978 .49978 .49979 .49980 .49981 .49981 .49982 .49983 .499833.6 .49984 .49985 .49985 .49986 .49986 .49987 .49987 .49988 .49988 .499893.7 .49989 .49990 .49990 .49990 .49991 .49991 .49992 .49992 .49992 .499923.8 .49993 .49993 .49993 .49994 .49994 .49994 .49994 .49995 .49995 .499953.9 .49995 .49995 .49996 .49996 .49996 .49996 .49996 .49996 .49997 .49997 NOTE:Some instructors prefer to use a different table, the Cumulative Standardized Normal Distribution (which represents the areas under the standardized normal distribution from to Z). The procedures and calculations using the two tables will be slightly different, but they will lead you to the same answers. 17Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study GuideTABLE 2 Critical Values of tIn this program, Dr. Levine uses a table of the t Distribution like that shown below.For a particular value of degrees of freedom df, each entry in this table representsthe critical value of t corresponding to a specific upper-tail area . 0.25 0.10 0.05 0.025 0.01 0.0051 1.0000 3.0777 6.3138 12.7062 31.8207 63.65742 0.8165 1.8856 2.9200 4.3027 6.9646 9.92483 0.7649 1.6377 2.3534 3.1824 4.5407 5.84094 0.7407 1.5332 2.1318 2.7764 3.7469 4.60415 0.7267 1.4759 2.0150 2.5706 3.3649 4.03226 0.7176 1.4398 1.9432 2.4469 3.1427 3.70747 0.7111 1.4149 1.8946 2.3646 2.9980 3.49958 0.7064 1.3968 1.8595 2.3060 2.8965 3.35549 0.7027 1.3830 1.8331 2. 2622 2.8214 3. 249810 0.6998 1.3722 1.8125 2. 2281 2.7638 3.169311 0.6974 1.3634 1.7959 2. 2010 2.7181 3.105812 0.6955 1.3562 1.7823 2.1788 2.6810 3.054513 0.6938 1.3502 1.7709 2.1604 2.6503 3.012314 0.6924 1.3450 1.7613 2.1448 2.6245 2.976815 0.6912 1.3406 1.7531 2.1315 2.6025 2.946716 0.6901 1.3368 1.7459 2.1199 2.5835 2.920817 0.6892 1.3334 1.7396 2.1098 2.5669 2.898218 0.6884 1.3304 1.7341 2.1009 2.5524 2.878419 0.6876 1.3277 1.7291 2.0930 2.5395 2.860920 0.6870 1.3253 1.7247 2.0860 2.5280 2.845321 0.6864 1.3232 1.7207 2.0796 2.5177 2.831422 0.6858 1.3212 1.7171 2.0739 2.5083 2.818823 0.6853 1.3195 1.7139 2.0687 2.4999 2.807324 0.6848 1.3178 1.7109 2.0639 2.4922 2.796925 0.6844 1.3163 1.7081 2.0595 2.4851 2.787426 0.6840 1.3150 1.7056 2.0555 2.4786 2.778727 0.6837 1.3137 1.7033 2.0518 2.4727 2.770728 0.6834 1.3125 1.7011 2.0484 2.4671 2.763329 0.6830 1.3114 1.6991 2.0452 2.4620 2.756430 0.6828 1.3104 1.6973 2.0423 2.4573 2.750031 0.6825 1.3095 1.6955 2.0395 2.4528 2.744032 0.6822 1.3086 1.6939 2.0369 2.4487 2.738533 0.6820 1.3077 1.6924 2.0345 2.4448 2.733334 0.6818 1.3070 1.6909 2.0322 2.4411 2.728435 0.6816 1.3062 1.6896 2.0301 2.4377 2.723836 0.6814 1.3055 1.6883 2.0281 2.4345 2.719537 0.6812 1.3049 1.6871 2.0262 2.4314 2.715438 0.6810 1.3042 1.6860 2.0244 2.4286 2.711639 0.6808 1.3036 1.6849 2.0227 2.4258 2.707940 0.6807 1.3031 1.6839 2.0211 2.4233 2.7045df18Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study Guide0.25 0.10 0.05 0.025 0.01 0.00541 0.6805 1.3025 1.6829 2.0195 2.4208 2.701242 0.6804 1.3020 1.6820 2.0181 2.4185 2.698143 0.6802 1.3016 1.6811 2.0167 2.4163 2.695144 0.6801 1.3011 1.6802 2.0154 2.4141 2.692345 0.6800 1.3006 1.6794 2.0141 2.4121 2.689646 0.6799 1.3022 1.6787 2.0129 2.4102 2.687047 0.6797 1. 2998 1.6779 2.0117 2.4083 2.684648 0.6796 1. 2994 1.6772 2.0106 2.4066 2.682249 0.6795 1. 2991 1.6766 2.0096 2.4049 2.680050 0.6794 1. 2987 1.6759 2.0086 2.4033 2.677851 0.6793 1. 2984 1.6753 2.0076 2.4017 2.675752 0.6792 1. 2980 1.6747 2.0066 2.4002 2.673753 0.6791 1. 2977 1.6741 2.0057 2.3988 2.671854 0.6791 1. 2974 1.6736 2.0049 2.3974 2.670055 0.6790 1. 2971 1.6730 2.0040 2.3961 2.668256 0.6789 1. 2969 1.6725 2.0032 2.3948 2.666557 0.6788 1. 2966 1.6720 2.0025 2.3936 2.664958 0.6787 1. 2963 1.6716 2.0017 2.3924 2.663359 0.6787 1. 2961 1.6711 2.0010 2.3912 2.661860 0.6786 1. 2958 1.6706 2.0003 2.3901 2.660361 0.6785 1. 2956 1.6702 1.9996 2.3890 2.658962 0.6785 1. 2954 1.6698 1.9990 2.3880 2.657563 0.6784 1. 2951 1.6694 1.9983 2.3870 2.656164 0.6783 1. 2949 1.6690 1.9977 2.3860 2.654965 0.6783 1. 2947 1.6686 1.9971 2.3851 2.653666 0.6782 1. 2945 1.6683 1.9966 2.3842 2.652467 0.6782 1. 2943 1.6679 1.9960 2.3833 2.651268 0.6781 1. 2941 1.6676 1.9955 2.3824 2.650169 0.6781 1. 2939 1.6672 1.9949 2.3816 2.649070 0.6780 1. 2938 1.6669 1.9944 2.3808 2.647971 0.6780 1. 2936 1.6666 1.9939 2.3800 2.646972 0.6779 1. 2934 1.6663 1.9935 2.3793 2.645973 0.6779 1. 2933 1.6660 1.9930 2.3785 2.644974 0.6778 1. 2931 1.6657 1.9925 2.3778 2.643975 0.6778 1. 2929 1.6654 1.9921 2.3771 2.643076 0.6777 1. 2928 1.6652 1.9917 2.3764 2.642177 0.6777 1. 2926 1.6649 1.9913 2.3758 2.641278 0.6776 1. 2925 1.6646 1.9908 2.3751 2.640379 0.6776 1. 2924 1.6644 1.9905 2.3745 2.639580 0.6776 1. 2922 1.6641 1.9901 2.3739 2.63870.6745 1. 2816 1.6449 1.9600 2.3263 2.5758TABLE 2 Critical Values of t (continued)df 19Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study GuideTABLE 3 Critical Values of 2In this program, Dr. Levine uses a table of the 2 Distribution like that shown below.For a particular value of degrees of freedom df, each entry in this table representsthe critical value of 2 corresponding to a specific upper-tail area .0.9950.990.9750.950.900.750.250.100.050.0250.010.00510.0010.0040.0160.1021.3232.7063.8415.0246.6357.87920.0100.0200.0510.1030.2110.5752.7734.6055.9917.3789.21010.59730.0720.1150.2160.3520.5841.2134.1086.2517.8159.34811.34512.83840.2070.2970.4840.7111.0641.9235.3857.7799.48811.14313.27714.86050.4120.5540.8311.1451.6102.6756.6269.23611.07112.83315.08616.75060.6760.8721.2371.6352.2043.4557.84110.64512.59214.44916.81218.45870.9891.2391.6902.1672.8334.2559.03712.01714.06716.01318.47520.27881.3441.6462.1802.7333.4905.07110.21913.36215.50717.53520.09021.95591.7352.0882.7003.3254.1685.89911.38914.68416.91919.02321.66623.589102.1562.5583.2473.9404.8656.73712.54915.98718.30720.48323.20925.188112.6033.0533.8164.5755.5787.58413.70117.27519.67521.92024.72526.757123.0743.5714.4045.2266.3048.43814.84518.54921.02623.33726.21728.299133.5654.1075.0095.8927.0429.29915.98419.81222.36224.73627.68829.819144.0754.6605.6296.5717.79010.16517.11721.06423.68526.11929.14131.319154.6015.2296.2627.2618.54711.03718.24522.30724.99627.48830.57832.801165.1425.8126.9087.9629.31211.91219.36923.54226.29628.84532.00034.267175.6976.4087.5648.67210.08512.79220.48924.76927.58730.19133.40935.718186.2657.0158.2319.39010.86513.67521.60525.98928.86931.52634.80537.156196.8447.6338.90710.11711.65114.56222.71827.20430.14432.85236.19138.582207.4348.2609.59110.85112.44315.45223.82828.41231.41034.17037.56639.997218.0348.89710.28311.59113.24016.34424.93529.61532.67135.47938.93241.401228.6439.54210.98212.33814.04217.24026.03930.81333.92436.78140.28942.796239.26010.19611.68913.09114.84818.13727.14132.00735.17238.07641.63844.181249.88610.85612.40113.84815.65919.03728.24133.19636.41539.36442.98045.5592510.52011.52413.12014.61116.47319.93929.33934.38237.65240.64644.31446.9282611.16012.19813.84415.37917.29220.84330.43535.56338.88541.92345.64248.2902711.80812.87914.57316.15118.11421.74931.52836.74140.11343.19446.96349.6452812.46113.56515.30816.92818.93922.65732.62037.91641.33744.46148.27850.9932913.12114.25716.04717.70819.76823.56733.71139.08742.55745.72249.58852.3363013.78714.95416.79118.49320.59924.47834.80040.25643.77346.97950.89253.672df 1 For larger values of freedom df, the expression Zdf=2212() may be used and the resultingupper-tail area can be found from the Cumulative Standardized Normal Distribution.20Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study GuideTABLE 4A Critical Values of F (where = 0.05)In this program, Dr. Levine uses a table of the F Distribution like that shown below.For a particular combination of numerator degrees of freedom df1 and denominatordegrees of freedom df1, each entry in this table represents the critical values of Fcorresponding to an upper-tail area equal to 0.05.1 2 3 4 5 6 7 8 9 101 161.40 199.50 215.70 224.60 230.20 234.00 236.80 238.90 240.50 241.90 254.302 18.51 19.00 19.16 19. 25 19.30 19.33 19.35 19.37 19.38 19.40 19.503 10.13 9.55 9. 28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.534 7.71 6.94 6.59 6.39 6. 26 6.16 6.09 6.04 6.00 5.96 5.635 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.366 5.99 5.14 4.76 4.53 4.39 4. 28 4. 21 4.15 4.10 4.06 3.677 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3. 238 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 2.939 5.12 4. 26 3.86 3.63 3.48 3.37 3. 29 3. 23 3.18 3.14 2.7110 4.96 4.10 3.71 3.48 3.33 3. 22 3.14 3.07 3.02 2.98 2.5411 4.84 3.98 3.59 3.36 3. 20 3.09 3.01 2.95 2.90 2.85 2.4012 4.75 3.89 3.49 3. 26 3.11 3.00 2.91 2.85 2.80 2.75 2.3013 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2. 2114 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.1315 4.54 3.68 3. 29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.0716 4.49 3.63 3. 24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.0117 4.45 3.59 3. 20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 1.9618 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 1.9219 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 1.8820 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 1.8421 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 1.8122 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 1.7823 4. 28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2. 27 1.7624 4. 26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2. 25 1.7325 4. 24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2. 28 2. 24 1.7126 4. 23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2. 27 2. 22 1.6927 4. 21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2. 25 2. 20 1.6728 4. 20 3.34 2.95 2.71 2.56 2.45 2.36 2. 29 2. 24 2.19 1.6529 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2. 28 2. 22 2.18 1.6430 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2. 27 2. 21 2.16 1.623.84 3.00 2.60 2.37 2. 21 2.10 2.01 1.94 1.88 1.83 1.00df1df2 = 0.05 1 = 0.9521Copyright 2007 Video Aided Instruction, Inc. All Rights ReservedThis study guide should be used along with a program published by Video Aided Instruction, Inc. For more information, call 1-800-238-1512 or visit us online at videoaidedinstruction.com.Statistics Study GuideTABLE 4B Critical Values of F (where = 0.01)In this program, Dr. Levine uses a table of the F Distribution like that shown below.For a particular combination of numerator degrees of freedom df1 and denominatordegrees of freedom df1, each entry in this table represents the critical values of Fcorresponding to an upper-tail area equal to 0.01.1234567891014,052.004,999.505,403.005,625.005,764.005,859.005,928.005,982.006,022.006,056.006,366.00298.5099.0099.1799.2599.3099.3399.3699.3799.3999.4099.50334.1230.8229.4628.7128.2427.9127.6727.4927.3527.2326.13421.2018.0016.6915.9815.5215.2114.9814.8014.6614.5513.46516.2613.2712.0611.3910.9710.6710.4610.2910.1610.059.02613.7510.929.789.158.758.478.268.107.987.876.88712.259.558.457.857.467.196.996.846.726.625.65811.268.657.597.016.636.376.186.035.915.814.86910.568.026.996.426.065.805.615.475.355.264.311010.047.566.555.995.645.395.205.064.944.853.91119.657.216.225.675.325.074.894.744.634.543.60129.336.935.955.415.064.824.644.504.394.303.36139.076.705.745.214.864.624.444.304.194.103.17148.866.515.565.044.694.464.284.144.033.943.00158.686.365.424.894.564.324.144.003.893.802.87168.536.235.294.774.444.204.033.893.783.692.75178.406.115.184.674.344.103.933.793.683.592.65188.296.015.094.584.254.013.843.713.603.512.57198.185.935.014.504.173.943.773.633.523.432.49208.105.854.944.434.103.873.703.563.463.372.42218.025.784.874.374.043.813.643.513.403.312.36227.955.724.824.313.993.763.593.453.353.262.31237.885.664.764.263.943.713.543.413.303.212.26247.825.614.724.223.903.673.503.363.263.172.21257.775.574.684.183.853.633.463.323.223.132.17267.725.534.644.143.823.593.423.293.183.092.13277.685.494.604.113.783.563.393.263.153.062.10287.645.454.574.073.753.533.363.233.123.032.06297.605.424.544.043.733.503.333.203.093.002.03307.565.394.514.023.703.473.303.173.072.982.016.634.613.783.323.022.802.642.512.412.321.00df1df2 = 0.01 1 = 0.99