Review for 1 sample CI Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.


 Leslie Stokes
 2 years ago
 Views:
Transcription
1 Review for 1 sample CI Name MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Fid the margi of error for the give cofidece iterval. 1) A survey foud that 69% of a radom sample of 1024 America adults approved of cloig edagered aimals. Fid the margi of error for this survey if we wat 90% cofidece i our estimate of the percet of America adults who approve of cloig edagered aimals. A) 4.27% B) 2.38% C) 2.83% D) 24.35% E) 5.09% 2) A recet poll of 1500 ew home buyers foud that 60% hired a movig compay to help them move to their ew home. Fid the margi of error for this poll if we wat 99% cofidece i our estimate of the percet of ew home buyers who hired movers. A) 1% B) 6.52% C) 4.96% D) 0.5% E) 3.26% Use the give degree of cofidece ad sample data to costruct a cofidece iterval for the populatio proportio. 3) Of 346 items tested, 12 are foud to be defective. Costruct a 98% cofidece iterval for the percetage of all such items that are defective. A) (0.13%, 6.80%) B) (1.85%, 5.09%) C) (0.93%, 6.00%) D) (3.34%, 3.59%) E) (1.18%, 5.76%) 4) A survey of 300 uio members i New York State reveals that 112 favor the Republica cadidate for goveror. Costruct a 98% cofidece iterval for the percetage of all New York State uio members who favor the Republica cadidate. A) (30.1%, 44.5%) B) (17.8%, 56.8%) C) (31.9%, 42.8%) D) (30.8%, 43.8%) E) (26.7%, 47.9%) Solve the problem. 5) A pollster wishes to estimate the true proportio of U.S. voters who oppose capital puishmet. How may voters should be surveyed i order to be 95% cofidet that the true proportio is estimated to withi 3%? A) 752 B) 1068 C) 1842 D) 1503 E) Not eough iformatio is give. 6) A uiversityʹs admiistrator proposes to do a aalysis of the proportio of graduates who have ot foud employmet i their major field oe year after graduatio. I previous years, the percetage averaged 13%. He wats the margi of error to be withi 4% at a 99% cofidece level. What sample size will suffice? A) 469 B) 19 C) 563 D) E) 272 1
2 Provide a appropriate respose. 7) I a survey of 1,000 televisio viewers, 40% said they watch etwork ews programs. For a 90% cofidece level, the margi of error for this estimate is 2.5%. If we wat to be 95% cofidet, how will the margi of error chage? A) Sice more cofidece requires a more arrow iterval, the margi of error will be smaller. B) Sice more cofidece requires a more arrow iterval, the margi of error will be larger. C) Sice more cofidece requires a wider iterval, the margi of error will be smaller. D) Sice more cofidece requires a wider iterval, the margi of error will be larger. E) There is ot eough iformatio to determie the effect o the margi of error. Usig the ttables, software, or a calculator, estimate the critical value of t for the give cofidece iterval ad degrees of freedom. 8) 90% cofidece iterval with df = 4. A) B) C) D) E) Iterpret the cofidece iterval. 9) Aalysis of a radom sample of 250 Illiois urses produced a 95% cofidece iterval for the mea aual salary of $42,803 < μ(nurse Salary) < $49,692. A) If we took may radom samples of Illiois urses, about 95% of them would produce this cofidece iterval. B) We are 95% cofidet that the average urse salary i the U.S. is betwee $42,803 ad $49,692. C) We are 95% cofidet that the iterval from $42,803 to $49,692 cotais the true mea salary of all Illiois urses. D) About 95% of Illiois urses ear betwee $42,803 ad $49,692. E) About 95% of the urses surveyed ear betwee $42,803 ad $49,692. Provide a appropriate respose. 10) You wat to determie if the average gas price i your city has exceeded $2.15 per gallo for regular gas. You take a radom sample of prices from 8 gas statios, recordig the followig prices: $2.13, $2.10, $1.80, $2.09, $2.17, $2.12, $2.10, $2.11. Have the coditios ad assumptios for iferece bee met? A) No, the sample is ot radom. B) No, the sample is ot represetative. C) Yes, all coditios ad assumptios have bee met. D) No, the sample is more tha 10% of the populatio. E) No, the early ormal coditio is ot met. 11) How may upopped kerels are left whe you pop a bag of microwave popcor? Each day, quality cotrol persoel take a radom sample of 50 bags of popcor. They pop each bag i a microwave ad the cout the umber of upopped kerels. Have the coditios ad assumptios for iferece bee met? A) Yes, all coditios ad assumptio are met. B) No, the sample is more tha 10% of the populatio size. C) No, this is ot a represetative sample sice the quality cotrol persoel work for the compay ad are biased. D) No, the sample does ot meet the Nearly Normal coditio. E) No, the sample is ot likely to be represetative. Use the give sample data to costruct the idicated cofidece iterval for the populatio mea. 12) = 10, x = 13.7, s = 4.4 Fid a 95% cofidece iterval for the mea. A) (10.60, 16.80) B) (10.60, 16.83) C) (10.57, 16.83) D) (11.15, 16.25) E) (10.55, 16.85) 2
3 13) A savigs ad loa associatio eeds iformatio cocerig the checkig accout balaces of its local customers. A radom sample of 14 accouts was checked ad yielded a mea balace of $ ad a stadard deviatio of $ Fid a 98% cofidece iterval for the true mea checkig accout balace for local customers. A) ($453.56, $874.72) B) ($492.52, $835.76) C) ($455.65, $835.76) D) ($455.65, $872.63) E) ($493.71, $834.57) Use the give sample data to costruct the idicated cofidece iterval for the populatio mea. 14) The pricipal radomly selected six studets to take a aptitude test. Their scores were: Determie a 90% cofidece iterval for the mea score for all studets. A) (82.90, 72.27) B) (72.37, 82.80) C) (82.80, 82.80) D) (82.80, 72.37) E) (72.27, 82.90) SHORT ANSWER. Write the word or phrase that best completes each statemet or aswers the questio. A statistics professor asked her studets whether or ot they were registered to vote. I a sample of 50 of her studets (radomly sampled from her 700 studets), 35 said they were registered to vote. 15) Fid a 95% cofidece iterval for the true proportio of the professorʹs studets who were registered to vote. (Make sure to check ay ecessary coditios ad to state a coclusio i the cotext of the problem.) 16) Explai what 95% cofidece meas i this cotext. 17) What is the probability that the true proportio of the professorʹs studets who were registered to vote is i your cofidece iterval? 18) Accordig to a September 2004 Gallup poll, about 73% of 18 to 29yearolds said that they were registered to vote. Does the 73% figure from Gallup seem reasoable for the professorʹs class? Explai. 19) If the professor oly kew the iformatio from the September 2004 Gallup poll ad wated to estimate the percetage of her studets who were registered to vote to withi ±4% with 95% cofidece, how may studets should she sample? The coutries of Europe report that 46% of the labor force is female. The Uited Natios woders if the percetage of females i the labor force is the same i the Uited States. Represetatives from the Uited States Departmet of Labor pla to check a radom sample of over 10,000 employmet records o file to estimate a percetage of females i the Uited States labor force. 20) The represetatives from the Departmet of Labor wat to estimate a percetage of females i the Uited States labor force to withi ±5%, with 90% cofidece. How may employmet records should they sample? 21) They actually select a radom sample of 525 employmet records, ad fid that 229 of the people are females. Create the cofidece iterval. 22) Iterpret the cofidece iterval i this cotext. 23) Explai what 90% cofidece meas i this cotext. 3
4 24) Should the represetatives from the Departmet of Labor coclude that the percetage of females i their labor force is lower tha Europeʹs rate of 46%? Explai. A professor at a large uiversity believes that studets take a average of 15 credit hours per term. A radom sample of 24 studets i her class of 250 studets reported the followig umber of credit hours that they were takig: 25) Fid a 95% cofidece iterval for the umber of credit hours take by the studets i the professorʹs class. Iterpret your iterval. Textbook authors must be careful that the readig level of their book is appropriate for the target audiece. Some methods of assessig readig level require estimatig the average word legth. Weʹve radomly chose 20 words from a radomly selected page i Stats: Modelig the World ad couted the umber of letters i each word: 5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6 26) For a more defiitive evaluatio of readig level the editor wats to estimate the textʹs word legth to withi 0.5 letters with 98% cofidece. How may radomly selected words does she eed to use? 4
5 Aswer Key Testame: UNTITLED1 1) B 2) E 3) E 4) D 5) B 6) A 7) D 8) D 9) C 10) E 11) A 12) E 13) A 14) B 15) We have a radom sample of less tha 10% of the professorʹs studets, with 35 expected successes (registered) ad 15 expected failures (ot registered), so a Normal model applies. = 50, p^ = = 0.70, q^ = 1  p^ = 0.30, so SE(p^) = Our 95% cofidece iterval is: p^q^ = (0.70)(0.30) 50 p^ ± z*se(p^) = 0.70 ± 1.96(0.065) = 0.70 ± = to = We are 95% cofidet that betwee 57.3% ad 82.7% of the professorʹs studets are registered to vote. 16) If may radom samples were take, 95% of the cofidece itervals produced would cotai the actual percetage of the professorʹs studets who are registered to vote. 17) There is o probability ivolvedoce the iterval is costructed, the true proportio of the professorʹs studets who were registered to vote is i the iterval or it is ot. 18) The 73% figure from Gallup seems reasoable sice 73% lies i our cofidece iterval. pq 19) ME = z* 0.04 = 1.96 (0.73)(0.27) = (1.96) 2(0.73)(0.27) = = 474 (0.04)2 Note: Sice there are oly 700 studets i the professorʹs class, she caot sample this may studets without violatig the 10% coditio! p^q^ 20) ME = z* 0.05 = = (0.46)(0.54) (0.46)(0.54) 0.05 = They should sample at least 269 employmet records. 5
6 Aswer Key Testame: UNTITLED1 21) We have a radom sample of less tha 10% of the employmet records, with 229 successes (females) ad 296 failures (males), so a Normal model applies. p^q^ = 525, p^ = ad q^ = 0.564, so SE(p^) = = (0.436)(0.564) = margi of error: ME = z* SE(p^) =(1.645)(0.022) = Cofidece iterval: p^ ± ME = ± or (0.3998, ) 22) We are 90% cofidet that betwee 40.0% ad 47.2% of the employmet records from the Uited States labor force are for females. 23) If may radom samples were take, 90% of the cofidece itervals produced would cotai the actual percetage of all female employmet records i the Uited States labor force. 24) No. Sice 46% lies i the cofidece iterval, (0.3998, ), it is possible that the percetage of females i the labor force matches Europeʹs rate of 46% females i the labor force. 25) With the coditios satisfied (from Problem 1), we ca fid a titerval for mea credit hours. We kow: = 24, y = 16.6, ad s = So, SE(y) = = Our cofidece iterval has the form y ± t* = 16.6 ± 0.94, or to s. We have t* 23 = Our 95% cofidece iterval is the 16.6 ± We are 95% cofidet that the iterval to cotais the true mea umber of credit hours that studets i the professorʹs class are takig. 26) First Estimate: ME = z* SE(y) 0.5 = = Although ot ecessary, sice 157 is quite large, we could fid a better estimate usig t*140 = 2.353, from Table T. ME = t*140 SE(y) 0.5 = =
Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
More informationSection 7.2 Confidence Interval for a Proportion
Sectio 7.2 Cofidece Iterval for a Proportio Before ay ifereces ca be made about a proportio, certai coditios must be satisfied: 1. The sample must be a SRS from the populatio of iterest. 2. The populatio
More information1. C. The formula for the confidence interval for a population mean is: x t, which was
s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : pvalue
More informationPractice Problems for Test 3
Practice Problems for Test 3 Note: these problems oly cover CIs ad hypothesis testig You are also resposible for kowig the samplig distributio of the sample meas, ad the Cetral Limit Theorem Review all
More informationReview for Test 3. b. Construct the 90% and 95% confidence intervals for the population mean. Interpret the CIs.
Review for Test 3 1 From a radom sample of 36 days i a recet year, the closig stock prices of Hasbro had a mea of $1931 From past studies we kow that the populatio stadard deviatio is $237 a Should you
More informationCh 7.1 pg. 364 #11, 13, 15, 17, 19, 21, 23, 25
Math 7 Elemetary Statistics: A Brief Versio, 5/e Bluma Ch 7.1 pg. 364 #11, 13, 15, 17, 19, 1, 3, 5 11. Readig Scores: A sample of the readig scores of 35 fifthgraders has a mea of 8. The stadard deviatio
More informationDefinition. Definition. 72 Estimating a Population Proportion. Definition. Definition
7 stimatig a Populatio Proportio I this sectio we preset methods for usig a sample proportio to estimate the value of a populatio proportio. The sample proportio is the best poit estimate of the populatio
More informationCHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Means and Proportions
CHAPTER 8: CONFIDENCE INTERVAL ESTIMATES for Meas ad Proportios Itroductio: We wat to kow the value of a parameter for a populatio. We do t kow the value of this parameter for the etire populatio because
More informationConfidence Intervals
Cofidece Itervals Cofidece Itervals are a extesio of the cocept of Margi of Error which we met earlier i this course. Remember we saw: The sample proportio will differ from the populatio proportio by more
More information7.1 Inference for a Population Proportion
7.1 Iferece for a Populatio Proportio Defiitio. The statistic that estimates the parameter p is the sample proportio cout of successes i the sample ˆp = cout of observatios i the sample. Assumptios for
More informationConfidence Intervals and Sample Size
8/7/015 C H A P T E R S E V E N Cofidece Itervals ad Copyright 015 The McGrawHill Compaies, Ic. Permissio required for reproductio or display. 1 Cofidece Itervals ad Outlie 71 Cofidece Itervals for the
More informationInference on Proportion. Chapter 8 Tests of Statistical Hypotheses. Sampling Distribution of Sample Proportion. Confidence Interval
Chapter 8 Tests of Statistical Hypotheses 8. Tests about Proportios HT  Iferece o Proportio Parameter: Populatio Proportio p (or π) (Percetage of people has o health isurace) x Statistic: Sample Proportio
More informationSection 73 Estimating a Population. Requirements
Sectio 73 Estimatig a Populatio Mea: σ Kow Key Cocept This sectio presets methods for usig sample data to fid a poit estimate ad cofidece iterval estimate of a populatio mea. A key requiremet i this sectio
More informationOverview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals
Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of
More informationConfidence Intervals for the Population Mean
Cofidece Itervals Math 283 Cofidece Itervals for the Populatio Mea Recall that from the empirical rule that the iterval of the mea plus/mius 2 times the stadard deviatio will cotai about 95% of the observatios.
More informationUsing Excel to Construct Confidence Intervals
OPIM 303 Statistics Ja Stallaert Usig Excel to Costruct Cofidece Itervals This hadout explais how to costruct cofidece itervals i Excel for the followig cases: 1. Cofidece Itervals for the mea of a populatio
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationMath C067 Sampling Distributions
Math C067 Samplig Distributios Sample Mea ad Sample Proportio Richard Beigel Some time betwee April 16, 2007 ad April 16, 2007 Examples of Samplig A pollster may try to estimate the proportio of voters
More informationKey Ideas Section 81: Overview hypothesis testing Hypothesis Hypothesis Test Section 82: Basics of Hypothesis Testing Null Hypothesis
Chapter 8 Key Ideas Hypothesis (Null ad Alterative), Hypothesis Test, Test Statistic, Pvalue Type I Error, Type II Error, Sigificace Level, Power Sectio 81: Overview Cofidece Itervals (Chapter 7) are
More informationChapter 7: Confidence Interval and Sample Size
Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum
More information1 Correlation and Regression Analysis
1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationOnesample test of proportions
Oesample test of proportios The Settig: Idividuals i some populatio ca be classified ito oe of two categories. You wat to make iferece about the proportio i each category, so you draw a sample. Examples:
More informationConfidence Intervals for One Mean with Tolerance Probability
Chapter 421 Cofidece Itervals for Oe Mea with Tolerace Probability Itroductio This procedure calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) with
More informationThe following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles
The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio
More informationOMG! Excessive Texting Tied to Risky Teen Behaviors
BUSIESS WEEK: EXECUTIVE EALT ovember 09, 2010 OMG! Excessive Textig Tied to Risky Tee Behaviors Kids who sed more tha 120 a day more likely to try drugs, alcohol ad sex, researchers fid TUESDAY, ov. 9
More informationSTA 2023 Practice Questions Exam 2 Chapter 7 sec 9.2. Case parameter estimator standard error Estimate of standard error
STA 2023 Practice Questios Exam 2 Chapter 7 sec 9.2 Formulas Give o the test: Case parameter estimator stadard error Estimate of stadard error Samplig Distributio oe mea x s t (1) oe p ( 1 p) CI: prop.
More informationConfidence Intervals for the Mean of Nonnormal Data Class 23, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Cofidece Itervals for the Mea of Noormal Data Class 23, 8.05, Sprig 204 Jeremy Orloff ad Joatha Bloom Learig Goals. Be able to derive the formula for coservative ormal cofidece itervals for the proportio
More informationHypothesis Tests Applied to Means
The Samplig Distributio of the Mea Hypothesis Tests Applied to Meas Recall that the samplig distributio of the mea is the distributio of sample meas that would be obtaied from a particular populatio (with
More information1 Computing the Standard Deviation of Sample Means
Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.
More informationChapter 10. Hypothesis Tests Regarding a Parameter. 10.1 The Language of Hypothesis Testing
Chapter 10 Hypothesis Tests Regardig a Parameter A secod type of statistical iferece is hypothesis testig. Here, rather tha use either a poit (or iterval) estimate from a simple radom sample to approximate
More informationZTEST / ZSTATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown
ZTEST / ZSTATISTIC: used to test hypotheses about µ whe the populatio stadard deviatio is kow ad populatio distributio is ormal or sample size is large TTEST / TSTATISTIC: used to test hypotheses about
More informationStatistics Lecture 14. Introduction to Inference. Administrative Notes. Hypothesis Tests. Last Class: Confidence Intervals
Statistics 111  Lecture 14 Itroductio to Iferece Hypothesis Tests Admiistrative Notes Sprig Break! No lectures o Tuesday, March 8 th ad Thursday March 10 th Exteded Sprig Break! There is o Stat 111 recitatio
More information15.075 Exam 3. Instructor: Cynthia Rudin TA: Dimitrios Bisias. November 22, 2011
15.075 Exam 3 Istructor: Cythia Rudi TA: Dimitrios Bisias November 22, 2011 Gradig is based o demostratio of coceptual uderstadig, so you eed to show all of your work. Problem 1 A compay makes highdefiitio
More informationText&Tests5. Project Maths SUPPLEMENT. Frances O Regan O. D. Morris. Leaving Certificate Higher Level Maths
Project Maths SUPPLEMENT Text&Tests5 Leavig Certificate Higher Level Maths Cotais all the Deferred Material ad Cetral Limit Theorem Fraces O Rega O. D. Morris O.D. Morris, Fraces O Rega, 2014 All rights
More information23.3 Sampling Distributions
COMMON CORE Locker LESSON Commo Core Math Stadards The studet is expected to: COMMON CORE SIC.B.4 Use data from a sample survey to estimate a populatio mea or proportio; develop a margi of error through
More informationAP * Statistics Review. Inference
AP * Statistics Review Iferece Teacher Packet AP* is a trademark of the College Etrace Examiatio Board. The College Etrace Examiatio Board was ot ivolved i the productio of this material. Copyright 009
More information5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
More informationCenter, Spread, and Shape in Inference: Claims, Caveats, and Insights
Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the
More informationˆ p 2. ˆ p 1. ˆ p 3. p 4. ˆ p 8
Sectio 8 1C The Techiques of Hypothesis Testig A claim is made that 10% of the populatio is left haded. A alterate claim is made that less tha 10% of the populatio is left haded. We will use the techiques
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More information0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9%
Sectio 10 Aswer Key: 0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1) A simple radom sample of New Yorkers fids that 87 are
More informationHypothesis testing in a Nutshell
Hypothesis testig i a Nutshell Summary by Pamela Peterso Drake Itroductio The purpose of this readig is to discuss aother aspect of statistical iferece, testig. A is a statemet about the value of a populatio
More informationAQA STATISTICS 1 REVISION NOTES
AQA STATISTICS 1 REVISION NOTES AVERAGES AND MEASURES OF SPREAD www.mathsbox.org.uk Mode : the most commo or most popular data value the oly average that ca be used for qualitative data ot suitable if
More informationUnit 20 Hypotheses Testing
Uit 2 Hypotheses Testig Objectives: To uderstad how to formulate a ull hypothesis ad a alterative hypothesis about a populatio proportio, ad how to choose a sigificace level To uderstad how to collect
More informationExplore Identifying Likely Population Proportions
COMMON CORE Locker LESSON Cofidece Itervals ad Margis of Error Commo Core Math Stadards The studet is expected to: COMMON CORE SIC.B.4 Use data from a sample survey to estimate a populatio mea or proportio;
More informationUniversity of California, Los Angeles Department of Statistics. Distributions related to the normal distribution
Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chisquare (χ ) distributio.
More informationCHAPTER 8. Confidence Interval Estimation LEARNING OBJECTIVES. USING Saxon Home Improvement
CHAPTER 8 Cofidece Iterval Estimatio USING STATISTICS @ Saxo Home Improvemet 8.1 CONFIDENCE INTERVAL ESTIMATION FOR THE MEAN (* KNOWN) 8.2 CONFIDENCE INTERVAL ESTIMATION FOR THE MEAN (* UNKNOWN) Studet
More informationPSYCHOLOGICAL STATISTICS
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics
More informationStat 104 Lecture 16. Statistics 104 Lecture 16 (IPS 6.1) Confidence intervals  the general concept
Statistics 104 Lecture 16 (IPS 6.1) Outlie for today Cofidece itervals Cofidece itervals for a mea, µ (kow σ) Cofidece itervals for a proportio, p Margi of error ad sample size Review of mai topics for
More informationSampling Distribution And Central Limit Theorem
() Samplig Distributio & Cetral Limit Samplig Distributio Ad Cetral Limit Samplig distributio of the sample mea If we sample a umber of samples (say k samples where k is very large umber) each of size,
More informationMeasures of Central Tendency
Measures of Cetral Tedecy A studet s grade will be determied by exam grades ( each exam couts twice ad there are three exams, HW average (couts oce, fial exam ( couts three times. Fid the average if the
More informationConfidence Interval for a Population Proportion
Coexios module: m46999 1 Cofidece Iterval for a Populatio Proportio OpeStax College This work is produced by The Coexios Project ad licesed uder the Creative Commos Attributio Licese 3.0 Durig a electio
More informationHypothesis Testing. Definitions. H 0 : The Null Hypothesis This is the hypothesis or claim that is initially assumed to be true.
Hypothesis Testig Hypothesis testig allows us to use a sample to decide betwee two statemets made about a Populatio characteristic. These two statemets are called the Null Hypothesis ad the Alterative
More informationInstitute for the Advancement of University Learning & Department of Statistics
Istitute for the Advacemet of Uiversity Learig & Departmet of Statistics Descriptive Statistics for Research (Hilary Term, 00) Lecture 5: Cofidece Itervals (I.) Itroductio Cofidece itervals (or regios)
More informationFM4 CREDIT AND BORROWING
FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer
More informationA Resource for Freestanding Mathematics Qualifications Working with %
Ca you aswer these questios? A savigs accout gives % iterest per aum.. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%
More informationCase Study. Normal and t Distributions. Density Plot. Normal Distributions
Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca
More informationConfidence Intervals
1 Cofidece Itervals Recall: Iferetial statistics are used to make predictios ad decisios about a populatio based o iformatio from a sample. The two major applicatios of iferetial statistics ivolve the
More informationProbability & Statistics Chapter 9 Hypothesis Testing
I Itroductio to Probability & Statistics A statisticia s most importat job is to draw ifereces about populatios based o samples take from the populatio Methods for drawig ifereces about parameters: ) Make
More informationEconomics 140A Confidence Intervals and Hypothesis Testing
Ecoomics 140A Cofidece Itervals ad Hypothesis Testig Obtaiig a estimate of a parameter is ot the al purpose of statistical iferece because it is highly ulikely that the populatio value of a parameter is
More informationResearch Method (I) Knowledge on Sampling (Simple Random Sampling)
Research Method (I) Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact
More informationI. Chisquared Distributions
1 M 358K Supplemet to Chapter 23: CHISQUARED DISTRIBUTIONS, TDISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad tdistributios, we first eed to look at aother family of distributios, the chisquared distributios.
More informationME 101 Measurement Demonstration (MD 1) DEFINITIONS Precision  A measure of agreement between repeated measurements (repeatability).
INTRODUCTION This laboratory ivestigatio ivolves makig both legth ad mass measuremets of a populatio, ad the assessig statistical parameters to describe that populatio. For example, oe may wat to determie
More informationStatistical Inference: Hypothesis Testing for Single Populations
Chapter 9 Statistical Iferece: Hypothesis Testig for Sigle Populatios A foremost statistical mechaism for decisio makig is the hypothesis test. The cocept of hypothesis testig lies at the heart of iferetial
More informationStandard Errors and Confidence Intervals
Stadard Errors ad Cofidece Itervals Itroductio I the documet Data Descriptio, Populatios ad the Normal Distributio a sample had bee obtaied from the populatio of heights of 5yearold boys. If we assume
More informationThis document contains a collection of formulas and constants useful for SPC chart construction. It assumes you are already familiar with SPC.
SPC Formulas ad Tables 1 This documet cotais a collectio of formulas ad costats useful for SPC chart costructio. It assumes you are already familiar with SPC. Termiology Geerally, a bar draw over a symbol
More informationConfidence interval, samplesize formula and test statistic, concerning:
Cofidece iterval, ampleize formula ad tet tatitic, cocerig: Populatio mea : (large ample, >30): z ± c z = c E Replace by F if available (rare). µ 0 EXAMPLE: A radom ample of 55 from a pecific populatio
More informationCHAPTER 11 Financial mathematics
CHAPTER 11 Fiacial mathematics I this chapter you will: Calculate iterest usig the simple iterest formula ( ) Use the simple iterest formula to calculate the pricipal (P) Use the simple iterest formula
More information3. Continuous Random Variables
Statistics ad probability: 31 3. Cotiuous Radom Variables A cotiuous radom variable is a radom variable which ca take values measured o a cotiuous scale e.g. weights, stregths, times or legths. For ay
More information3.1 Measures of Central Tendency. Introduction 5/28/2013. Data Description. Outline. Objectives. Objectives. Traditional Statistics Average
5/8/013 C H 3A P T E R Outlie 3 1 Measures of Cetral Tedecy 3 Measures of Variatio 3 3 3 Measuresof Positio 3 4 Exploratory Data Aalysis Copyright 013 The McGraw Hill Compaies, Ic. C H 3A P T E R Objectives
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationTIEE Teaching Issues and Experiments in Ecology  Volume 1, January 2004
TIEE Teachig Issues ad Experimets i Ecology  Volume 1, Jauary 2004 EXPERIMENTS Evirometal Correlates of Leaf Stomata Desity Bruce W. Grat ad Itzick Vatick Biology, Wideer Uiversity, Chester PA, 19013
More informationMEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book)
MEI Mathematics i Educatio ad Idustry MEI Structured Mathematics Module Summary Sheets Statistics (Versio B: referece to ew book) Topic : The Poisso Distributio Topic : The Normal Distributio Topic 3:
More informationStatistical Methods. Chapter 1: Overview and Descriptive Statistics
Geeral Itroductio Statistical Methods Chapter 1: Overview ad Descriptive Statistics Statistics studies data, populatio, ad samples. Descriptive Statistics vs Iferetial Statistics. Descriptive Statistics
More informationStatistical inference: example 1. Inferential Statistics
Statistical iferece: example 1 Iferetial Statistics POPULATION SAMPLE A clothig store chai regularly buys from a supplier large quatities of a certai piece of clothig. Each item ca be classified either
More informationLesson 15 ANOVA (analysis of variance)
Outlie Variability betwee group variability withi group variability total variability Fratio Computatio sums of squares (betwee/withi/total degrees of freedom (betwee/withi/total mea square (betwee/withi
More informationLesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) types of data scatter plots measure of directio measure of stregth Computatio covariatio of X ad Y uique variatio i X ad Y measurig
More informationQuadrat Sampling in Population Ecology
Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may
More informationMR. STEIN S WORDS OF WISDOM
MR. STEIN S WORDS OF WISDOM P a g e 1 I am writig this review essay for two tests the AP Stat exam ad the Applied Stat Fial exam. The topics are more or less the same, so reviewig for the two tests should
More informationSimple Linear Regression
Simple Liear Regressio We have bee itroduced to the otio that a categorical variable could deped o differet levels of aother variable whe we discussed cotigecy tables. We ll exted this idea to the case
More informationG r a d e. 2 M a t h e M a t i c s. statistics and Probability
G r a d e 2 M a t h e M a t i c s statistics ad Probability Grade 2: Statistics (Data Aalysis) (2.SP.1, 2.SP.2) edurig uderstadigs: data ca be collected ad orgaized i a variety of ways. data ca be used
More informationCompare Multiple Response Variables
Compare Multiple Respose Variables STATGRAPHICS Mobile Rev. 4/7/006 This procedure compares the data cotaied i three or more Respose colums. It performs a oeway aalysis of variace to determie whether
More informationChapter 10 Student Lecture Notes 101
Chapter 0 tudet Lecture Notes 0 Basic Busiess tatistics (9 th Editio) Chapter 0 Twoample Tests with Numerical Data 004 PreticeHall, Ic. Chap 0 Chapter Topics Comparig Two Idepedet amples Z test for
More informationCase Study. Contingency Tables. Graphing Tabled Counts. Stacked Bar Graph
Case Study Cotigecy Tables Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 4 6, 2011 Case Study Example 9.3 begiig o page 213 of the text describes a experimet i which
More information5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?
5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso
More informationLecture 23. Chapter 11: Testing Hypotheses About Proportions. Nancy Pfenning Stats 1000. Recall: last time we presented the following examples:
Lecture 23 Nacy Pfeig Stats 1000 Chapter 11: Testig Hypotheses About Proportios Recall: last time we preseted the followig examples: 1. I a group of Pitt studets, 42 were lefthaded. Is this sigificatly
More informationHypergeometric Distributions
7.4 Hypergeometric Distributios Whe choosig the startig lieup for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you
More informationNonlife insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring
Nolife isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy
More informationAnalyzing Longitudinal Data from Complex Surveys Using SUDAAN
Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical
More information7818 Interval estimation and hypothesis testing  Set
7 7818 Iterval estimatio ad hypothesis testig  Set revised Nov 9, 010 You might wat to read some of the chapter i MGB o Parametric Iterval Estimatio. There are subtle di ereces across questios. uderstad
More informationx : X bar Mean (i.e. Average) of a sample
A quick referece for symbols ad formulas covered i COGS14: MEAN OF SAMPLE: x = x i x : X bar Mea (i.e. Average) of a sample x i : X sub i This stads for each idividual value you have i your sample. For
More information, a Wishart distribution with n 1 degrees of freedom and scale matrix.
UMEÅ UNIVERSITET Matematiskstatistiska istitutioe Multivariat dataaalys D MSTD79 PA TENTAMEN 00409 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multivariat dataaalys D, 5 poäg.. Assume that
More informationMultiserver Optimal Bandwidth Monitoring for QoS based Multimedia Delivery Anup Basu, Irene Cheng and Yinzhe Yu
Multiserver Optimal Badwidth Moitorig for QoS based Multimedia Delivery Aup Basu, Iree Cheg ad Yizhe Yu Departmet of Computig Sciece U. of Alberta Architecture Applicatio Layer Request receptio coectio
More informationApproximating the Sum of a Convergent Series
Approximatig the Sum of a Coverget Series Larry Riddle Ages Scott College Decatur, GA 30030 lriddle@agesscott.edu The BC Calculus Course Descriptio metios how techology ca be used to explore covergece
More informationLaboratory: CaseControl Studies. Hypothesis Testing
Laboratory: CaseCotrol Studies How may do I eed? is oe of the most commo questios addressed to a epidemiologist. The epidemiologist aswers with What questio are you attemptig to aswer? Sample size depeds
More informationPredictive Modeling Data. in the ACT Electronic Student Record
Predictive Modelig Data i the ACT Electroic Studet Record overview Predictive Modelig Data Added to the ACT Electroic Studet Record With the release of studet records i September 2012, predictive modelig
More informationSAMPLING NTI Bulletin 2006,42/3&4, 5562
SAMPLING NTI Bulleti 006,4/3&4, 556 Sample size determiatio i health studies VK Chadha * Summary Oe of the most importat factors to cosider i the desig of a itervetio trial is the choice of a appropriate
More informationEstimating the Mean and Variance of a Normal Distribution
Estimatig the Mea ad Variace of a Normal Distributio Learig Objectives After completig this module, the studet will be able to eplai the value of repeatig eperimets eplai the role of the law of large umbers
More information