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### Chapter10

Course: ECONOMIC 102, Spring 2012
School: College of the Siskiyous
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for Statistics Managers Using Microsoft Excel 5th Edition Chapter 10 Two-Sample Tests Statistics for Managers Using Microsoft Excel, 5e 2008 Prentice-Hall, Inc. Chap 10-1 Learning Objectives In this chapter, you learn how to use hypothesis testing for comparing the difference between: The means of two independent populations The means of two related populations The proportions of two independent...

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for Statistics Managers Using Microsoft Excel 5th Edition Chapter 10 Two-Sample Tests Statistics for Managers Using Microsoft Excel, 5e 2008 Prentice-Hall, Inc. Chap 10-1 Learning Objectives In this chapter, you learn how to use hypothesis testing for comparing the difference between: The means of two independent populations The means of two related populations The proportions of two independent populations The variances of two independent populations Statistics for Managers Using Microsoft Excel, 5e Chap 10-2 Two-Sample Tests Overview Two Sample Tests Independent Population Means Means, Related Populations Independent Population Proportions Same group before vs. after treatment Proportion 1vs. Proportion 2 Independent Population Variances Examples Group 1 vs. Group 2 Statistics for Managers Using Microsoft Excel, 5e Variance 1 vs. Variance 2 Chap 10-3 Two-Sample Tests Independent Population Means 1 and 2 known 1 and 2 unknown Goal: Test hypothesis or form a confidence interval for the difference between two population means, 1 2 The point estimate for the difference between sample means: X1 X2 Statistics for Managers Using Microsoft Excel, 5e Chap 10-4 Two-Sample Tests Independent Populations Different data sources Independent Population Means 1 and 2 known 1 and 2 unknown Independent: Sample selected from one population has no effect on the sample selected from the other population Use the difference between 2 sample means Use Z test, pooled variance t test, or separate-variance t test Statistics for Managers Using Microsoft Excel, 5e Chap 10-5 Two-Sample Tests Independent Populations Independent Population Means 1 and 2 known 1 and 2 unknown Use a Z test statistic Use S to estimate unknown , use a t test statistic Statistics for Managers Using Microsoft Excel, 5e Chap 10-6 Two-Sample Tests Independent Populations Independent Population Means 1 and 2 known Assumptions: Samples are randomly and independently drawn population distributions are normal 1 and 2 unknown Statistics for Managers Using Microsoft Excel, 5e Chap 10-7 Two-Sample Tests Independent Populations Independent Population Means When 1 and 2 are known and both populations are normal, the test statistic is a Z-value and the standard error of X1 X2 is 1 and 2 known 2 1 and 2 unknown X1 X 2 Statistics for Managers Using Microsoft Excel, 5e 2 1 2 = + n1 n 2 Chap 10-8 Two-Sample Tests Independent Populations Independent Population Means 1 and 2 known The test statistic is: ( X X )( Z= 1 1 and 2 unknown Statistics for Managers Using Microsoft Excel, 5e 2 2 1 2 ) 2 1 2 + n1 n 2 Chap 10-9 Two-Sample Tests Independent Populations Two Independent Populations, Comparing Means Lower-tail test: Upper-tail test: Two-tail test: H0: 1 2 H1: 1 < 2 H0: 1 2 H1: 1 > 2 H0: 1 = 2 H 1 : 1 2 i.e., i.e., i.e., H0: 1 2 0 H1: 1 2 < 0 H0: 1 2 0 H 1 : 1 2 > 0 H0: 1 2 = 0 H1: 1 2 0 Statistics for Managers Using Microsoft Excel, 5e Chap 10-10 Two-Sample Tests Independent Populations Two Independent Populations, Comparing Means Lower-tail test: Upper-tail test: Two-tail test: H0: 1 2 0 H1: 1 2 < 0 H0: 1 2 0 H 1 : 1 2 > 0 -z Reject H0 if Z < -Za z Reject H0 if Z > Za Statistics for Managers Using Microsoft Excel, 5e H0: 1 2 = 0 H1: 1 2 0 /2 /2 -z/2 z/2 Reject H0 if Z < -Za/2 or Z > Za/2 Chap 10-11 Two-Sample Tests Independent Populations Independent Population Means Assumptions: Samples are randomly and independently drawn 1 and 2 known Populations are normally distributed 1 and 2 unknown Population variances are unknown but assumed equal Statistics for Managers Using Microsoft Excel, 5e Chap 10-12 Two-Sample Tests Independent Populations Independent Population Means 1 and 2 known 1 and 2 unknown Forming interval estimates: The population variances are assumed equal, so use the two sample standard deviations and pool them to estimate the test statistic is a t value with (n1 + n2 2) degrees of freedom Statistics for Managers Using Microsoft Excel, 5e Chap 10-13 Two-Sample Tests Independent Populations Independent Population Means 1 and 2 known The pooled standard deviation is: ( n1 1)S1 + ( n 2 1)S2 2 1 and 2 unknown Sp = Statistics for Managers Using Microsoft Excel, 5e (n1 1) + ( n 2 1) Chap 10-14 2 Two-Sample Tests Independent Populations Independent Population Means The test statistic is: ( X X )( t= 1 1 2 ) 1 1 S + n n 2 1 2 p 1 and 2 known 1 and 2 unknown 2 Where t has (n1 + n2 2) d.f., and ( n1 1) S12 + ( n2 1) S2 2 S2 = p Statistics for Managers Using Microsoft Excel, 5e (n1 1) + (n2 1) Chap 10-15 Two-Sample Tests Independent Populations You are a financial analyst for a brokerage firm. Is there a difference in dividend yield between stocks listed on the NYSE & NASDAQ? You collect the following data: NYSE NASDAQ Number 21 25 Sample mean 3.27 2.53 Sample std dev 1.30 1.16 Assuming both populations are approximately normal with equal variances, is there a difference in average yield ( = 0.05)? Statistics for Managers Using Microsoft Excel, 5e Chap 10-16 Two-Sample Tests Independent Populations The test statistic is: (X t= 1 ) X 2 ( 1 2 ) 1 1 S + n n 2 1 2 p = ( 3.27 2.53 ) 0 1 1 1.5021 + 21 25 = 2.040 ( n1 1)S12 + ( n2 1)S2 2 = ( 21 1)1.30 2 + ( 25 1)1.16 2 S2 = p (n1 1) + (n2 1) (21 - 1) + (25 1) Statistics for Managers Using Microsoft Excel, 5e = 1.5021 Chap 10-17 Two-Sample Tests Independent Populations H0: 1 - 2 = 0 i.e. (1 = 2) Reject H0 Reject H0 H1: 1 - 2 0 i.e. (1 2) = 0.05 .025 df = 21 + 25 - 2 = 44 -2.0154 Critical Values: t = 2.0154 Test Statistic: 2.040 .025 0 2.0154 t 2.040 Decision: Reject H0 at = 0.05 Conclusion: There is evidence of a difference in the means. Statistics for Managers Using Microsoft Excel, 5e Chap 10-18 Independent Populations Unequal Variance If you cannot assume population variances are equal, the pooled-variance t test is inappropriate Instead, use a separate-variance t test, which includes the two separate sample variances in the computation of the test statistic The computations are complicated and are best performed using Excel Statistics for Managers Using Microsoft Excel, 5e Chap 10-19 Two-Sample Tests Independent Populations Independent Population Means 1 and 2 known The confidence interval for 1 2 is: ( ) 2 2 1 2 X1 X 2 Z + n1 n 2 1 and 2 unknown Statistics for Managers Using Microsoft Excel, 5e Chap 10-20 Two-Sample Tests Independent Populations Independent Population Means The confidence interval for 1 2 is: ( X X ) t 1 2 1 and 2 known n1 + n 2 - 2 1 1 S + n n 2 1 2 p Where 1 and 2 unknown ( n1 1) S12 + ( n2 1) S2 2 S2 = p Statistics for Managers Using Microsoft Excel, 5e (n1 1) + (n2 1) Chap 10-21 Two-Sample Tests Related Populations Tests Means of 2 Related Populations Paired or matched samples Repeated measures (before/after) Use difference between paired values: D = X1 - X2 Eliminates Variation Among Subjects Assumptions: Both Populations Are Normally Distributed Statistics for Managers Using Microsoft Excel, 5e Chap 10-22 Two-Sample Tests Related Populations The ith paired difference is Di , where Di = X1i - X2i The point estimate for the population mean paired difference is D : n D= D i =1 i n Suppose the population standard deviation of the difference scores, D, is known. Statistics for Managers Using Microsoft Excel, 5e Chap 10-23 Two-Sample Tests Related Populations The test statistic for the mean difference is a Z value: D D Z= D n Where D = hypothesized mean difference D = population standard deviation of differences n = the sample size (number of pairs) Statistics for Managers Using Microsoft Excel, 5e Chap 10-24 Two-Sample Tests Related Populations If D is unknown, you can estimate the unknown population standard deviation with a sample standard deviation: n SD = (Di D) 2 i =1 n 1 Statistics for Managers Using Microsoft Excel, 5e Chap 10-25 Two-Sample Tests Related Populations The test statistic for D is now a t statistic: D D t= SD n n Where t has n - 1 d.f. and SD is: SD = Statistics for Managers Using Microsoft Excel, 5e (D i=1 i D) 2 n1 Chap 10-26 Two-Sample Tests Related Populations Lower-tail test: Upper-tail test: Two-tail test: H0: D 0 H 1 : D < 0 H0: D 0 H 1 : D > 0 H0: D = 0 H1: D 0 -t Reject H0 if t < -ta t Reject H0 if t > ta Statistics for Managers Using Microsoft Excel, 5e /2 /2 -t/2 t/2 Reject H0 if t < -ta/2 or t > ta/2 Chap 10-27 Two-Sample Tests Related Populations Example Assume you send your salespeople to a customer service training workshop. Has the training made a difference the in number of complaints? You collect the following data: Salesperson Number of Complaints Before (1) After (2) Difference, Di (2-1) C.B. 6 4 -2 T.F. 20 6 -14 M.H. 3 2 -1 R.K. 0 0 0 M.O 4 0 -4 Statistics for Managers Using Microsoft Excel, 5e Chap 10-28 Two-Sample Tests Related Populations Example Salesperson Number of Complaints Before (1) Difference, Di (2-1) After (2) C.B. 6 4 -2 T.F. 20 6 -14 M.H. 3 2 -1 R.K. 0 0 0 4 0 M.O n D= Di i =1 n = 4.2 SD = (D i D) -4 2 n 1 = 5.67 Statistics for Managers Using Microsoft Excel, 5e Chap 10-29 Two-Sample Tests Related Populations Example Has the training made a difference in the number of complaints (at the = 0.01 level)? H0: D = 0 H1: D 0 Critical Value = 4.604 d.f. = n - 1 = 4 Test Statistic: t= D D 4.2 0 = = 1.66 SD / n 5.67/ 5 Statistics for Managers Using Microsoft Excel, 5e Chap 10-30 Two-Sample Tests Related Populations Example Reject Reject /2 /2 - 4.604 4.604 - 1.66 Decision: Do not reject H0 (t statistic is not in the reject region) Conclusion: There is no evidence of a significant change in the number of complaints Statistics for Managers Using Microsoft Excel, 5e Chap 10-31 Two-Sample Tests Related Populations The confidence interval for D ( known) is: D DZ n Where n = the sample size (number of pairs in the paired sample) Statistics for Managers Using Microsoft Excel, 5e Chap 10-32 Two-Sample Tests Related Populations The confidence interval for D ( unknown) is: SD D t n1 n n where SD = (Di D)2 Statistics for Managers Using Microsoft Excel, 5e i=1 n 1 Chap 10-33 Two Population Proportions Goal: Test a hypothesis or form a confidence interval for the difference between two independent population proportions, 1 2 Assumptions: n11 5 , n1(1-1) 5 n22 5 , n2(1-2) 5 The point estimate for the difference is p1 - p2 Statistics for Managers Using Microsoft Excel, 5e Chap 10-34 Two Population Proportions Since you begin by assuming the null hypothesis is true, you assume 1 = 2 and pool the two sample (p) estimates. The pooled estimate for the overall proportion is: X1 + X 2 p= n1 + n 2 where X1 and X2 are the number of successes in samples 1 and 2 Statistics for Managers Using Microsoft Excel, 5e Chap 10-35 Two Population Proportions The test statistic for p1 p2 is a Z statistic: Z= where ( p1 p2 ) ( 1 2 ) 1 1 p (1 p) + n n 2 1 p= X1 + X 2 X X , P = 1 , P2 = 2 1 n1 + n 2 n1 n2 Statistics for Managers Using Microsoft Excel, 5e Chap 10-36 Two Population Proportions Hypothesis for Population Proportions Lower-tail test: Upper-tail test: Two-tail test: H0: 1 2 H 1 : 1 < 2 H0: 1 2 H1: 1 > 2 H0: 1 = 2 H 1: 1 2 i.e., i.e., i.e., H0: 1 2 0 H 1 : 1 2 < 0 H0: 1 2 0 H 1: 1 2 > 0 H0: 1 2 = 0 H 1 : 1 2 0 Statistics for Managers Using Microsoft Excel, 5e Chap 10-37 Two Population Proportions Hypothesis for Population Proportions Lower-tail test: Upper-tail test: Two-tail test: H0: 1 2 0 H 1 : 1 2 < 0 H0: 1 2 0 H 1: 1 2 > 0 H0: 1 2 = 0 H 1 : 1 2 0 -z Reject H0 if Z < -Z z Reject H0 if Z > Z Statistics for Managers Using Microsoft Excel, 5e /2 /2 -z/2 z/2 Reject H0 if Z < -Z/2 or Z > Z/2 Chap 10-38 Two Independent Population Proportions: Example Is there a significant difference between the proportion of men and the proportion of women who will vote Yes on Proposition A? In a random sample of 72 men, 36 indicated they would vote Yes and, in a sample of 50 women, 31 indicated they would vote Yes Test at the .05 level of significance Statistics for Managers Using Microsoft Excel, 5e Chap 10-39 Two Independent Population Proportions: Example H0: 1 2 = 0 (the two proportions are equal) H1: 1 2 0 (there is a significant difference between proportions) The sample proportions are: Men: p1 = 36/72 = .50 Women: p2 = 31/50 = .62 The pooled estimate for the overall proportion is: p= X1 + X 2 36 + 31 67 = = = .549 n1 + n 2 72 + 50 122 Statistics for Managers Using Microsoft Excel, 5e Chap 10-40 Two Independent Population Proportions: Example Reject H0 .025 The test statistic for 1 2 is: z= = ( p1 p2 ) ( 1 2 ) 1 1 p (1 p) + n n 2 1 ( .50 .62) ( 0) 1 1 .549 (1 .549) + 72 50 .025 -1.96 -1.31 = 1.31 Critical Values = 1.96 For = .05 Reject H0 1.96 Decision: Do not reject H0 Conclusion: There is no evidence of a significant difference in proportions who will vote yes between men and women. Statistics for Managers Using Microsoft Excel, 5e Chap 10-41 Two Independent Population Proportions The confidence interval for 1 2 is: ( p1 p2 ) Z p1 (1 p1 ) p2 (1 p2 ) + n1 n2 Statistics for Managers Using Microsoft Excel, 5e Chap 10-42 Testing Population Variances Purpose: To determine if two independent populations have the same variability. H0: 12 = 22 H1: 12 22 H0: 12 22 H1: 12 < 22 H0: 12 22 H1: 12 > 22 Two-tail test Lower-tail test Upper-tail test Statistics for Managers Using Microsoft Excel, 5e Chap 10-43 Testing Population Variances The F test statistic is: 2 1 2 2 S F= S 2 S1 = Variance of Sample 1 n1 - 1 = numerator degrees of freedom S 2 = Variance of Sample 2 2 n2 - 1 = denominator degrees of freedom Statistics for Managers Using Microsoft Excel, 5e Chap 10-44 Testing Population Variances The F critical value is found from the F table There are two appropriate degrees of freedom: numerator and denominator. In the F table, numerator degrees of freedom determine the column denominator degrees of freedom determine the row Statistics for Managers Using Microsoft Excel, 5e Chap 10-45 Testing Population Variances Lower-tail test Upper-tail test H0: 12 22 H1: 12 < 22 H0: 12 22 H1: 12 > 22 0 0 Reject H0 FL Do not reject H0 Reject H0 if F < FL Statistics for Managers Using Microsoft Excel, 5e Do not reject H0 FU Reject H0 Reject H0 if F > FU Chap 10-46 Testing Population Variances Two-tail test H0: 12 = 22 H1: 12 22 /2 /2 0 FL Do not reject H0 FU Reject H0 F rejection region for a two-tail test is: Statistics for Managers Using Microsoft Excel, 5e 2 S1 F = 2 > FU S2 2 S1 F = 2 < FL S2 Chap 10-47 Testing Population Variances To find the critical F values: 1. Find FU from the F table for n1 1 numerator and n2 1 denominator degrees of freedom. 2. Find FL using the formula: FL = 1 FU* Where FU* is from the F table with n2 1 numerator and n1 1 denominator degrees of freedom (i.e., switch the d.f. from FU) Statistics for Managers Using Microsoft Excel, 5e Chap 10-48 Testing Population Variances You are a financial analyst for a brokerage firm. You want to compare dividend yields between stocks listed on the NYSE & NASDAQ. You collect the following data: NYSE NASDAQ Number 21 25 Mean 3.27 2.53 Std dev 1.30 1.16 Is there a difference in the variances between the NYSE & NASDAQ at the = 0.05 level? Statistics for Managers Using Microsoft Excel, 5e Chap 10-49 Testing Population Variances Form the hypothesis test: H0: 21 22 = 0 (there is no difference between variances) H1: 21 22 0 (there is a difference between variances) FU: FL: Numerator: n1 1 = 21 1 = 20 d.f. Denominator: n2 1 = 25 1 = 24 d.f. Numerator: n2 1 = 25 1 = 24 d.f. Denominator: n1 1 = 21 1 = 20 d.f. FU = F.025, 20, 24 = 2.33 Statistics for Managers Using Microsoft Excel, 5e FL = 1/F.025, 24, 20 = 0.41 Chap 10-50 Testing Population Variances The test statistic is: S12 1.30 2 F= 2= = 1.256 2 S 2 1.16 /2 = .025 /2 = .025 0 Reject H0 Do not reject H0 FL=0.41 F = 1.256 is not in the rejection region, so we do not reject H0 Reject H0 FU=2.33 Conclusion: There is insufficient evidence of a difference in variances at = .05 Statistics for Managers Using Microsoft Excel, 5e Chap 10-51 F Chapter Summary In this chapter, we have Compared two independent samples Performed Z test for the differences in two means Performed pooled variance t test for the differences in two means Formed confidence intervals for the differences between two means Compared two related samples (paired samples) Performed paired sample Z and t tests for the mean difference Formed confidence intervals for the paired difference Performed separate-variance t test Statistics for Managers Using Microsoft Excel, 5e Chap 10-52 Chapter Summary In this chapter, we have Compared two population proportions Formed confidence intervals for the difference between two population proportions Performed Z-test for two population proportions Performed F tests for the difference between two population variances Used the F table to find F critical values Statistics for Managers Using Microsoft Excel, 5e Chap 10-53
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Name: _CECS 463 SOC IIDue: 2/14/2012Assignment #3: Sampling of WaveformsOften we must sample waveforms to obtain data for processing through filters. Here is an exercise ingenerating via Matlab waveforms of various shapes and periods.In each of the
CSU Long Beach - CECS - 463
Name: _CECS 463 SOC IIAssignment #4: Discrete Time SystemsDue: 2/28/20121. Generate and plot the samples (use stem function) of the following sequences using MATLAB()[ ()()](a) ( )(b) ( ) ( )()2. Let x(n)=cfw_1,-2,4,6,-5*,8,10. Generate and
CSU Long Beach - CECS - 463
Name: _CECS 463 SOC IIAssignment #6: Discrete Time Fourier TransformDue: March 22, 20121. Write a Matlab function to compute the DTFT of a finite duration sequence. The form of the functionshould be:function [X]=my_dtft(x,n,w)%Compute Discrete Time
CSU Long Beach - CECS - 463
Discrete Time Signals andSystemsCECS 463 Spring 2011Discrete Time SignalsSequence:x(n) = cfw_x(n)=cfw_, x(-1), x(0)*, x(1), where * indicates the sample at n=0.x(n) is a row vector of finite durationn vector indicates time indexes of samplesn=[-3
CSU Long Beach - CECS - 463
CECS 463System On ChipChapter 1 IntroductionDigital Signal Processing Using MATLAB and Wavelets, M.Weeks, Infinity Science Press, 2007, pp. 1-271IntroductionNumbersBase (Radix=R) n-digit form: N =(dn-1dn-1 d1d0)Base 10 (R=10) digits: 0,1,2 9 (DE
CSU Long Beach - CECS - 463
Lecture #2 PHASORS IN THE COMPLEX PLANE1. A vector r drawn in the complex plane. Let =t = 2ft where f is the linear frequency and is theangular frequency. Now increases with time and the vector r will rotate in the complex plane about theorigin at a ra
CSU Long Beach - CECS - 463
CECS 463System On ChipChapter 2 MATLABDigital Signal Processing Using MATLAB and Wavelets, M.Weeks, Infinity Science Press, 2007, pp. 29-841MATLAB BasicsScalars (or constants): a=3.5 or b=piVectors (row or column): c=[1 2] ord=[3;4]Matrices: A =
CSU Long Beach - CECS - 463
CECS 463System On ChipDiscrete Time FourierTransform1Discrete Time Fourier Transform2Examples3Two Important PropertiesPeriodicity: The DTFT is periodic in withperiod 2 like so: X(ej)= X(ej(+2)We only have to plot over [0,2 ] or [- ,]Symmetry:
CSU Long Beach - CECS - 463
clear all; clf;pause on; hold on;R=1*exp(j*30*pi/180); %Phasorf=1; T=1/f ; %Frequency of sinusoid phasork=[0:0.01:2*pi]; plot(cos(k),sin(k),'k'); grid; %Plot unit circlestep=T/100; %Step intervalfor n=1:101 t(n)=n*step; R=R*exp(j*2*pi*f*step); %A
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lear all; clf;pause on; hold on;fprintf('START\n');R=1*exp(j*30*pi/180); %Phasorfigure(1);for m=50:-5:5k=[0:0.01:2*pi]; plot(cos(k),sin(k),'k'); %Plot unit circle f=1; w=2*pi*f; T=1/f ; %Frequency of sinusoid phasorR=1*exp(j*30*pi/180); %Phasor p
CSU Long Beach - CECS - 463
CECS 463System On ChipChapter 1 IntroductionDigital Signal Processing Using MATLAB and Wavelets, M.Weeks, Infinity Science Press, 2007, pp. 1-271IntroductionNumbersBase (Radix=R) n-digit form: N =(dn-1dn-1 d1d0)Base 10 (R=10) digits: 0,1,2 9 (DE
CSU Long Beach - CECS - 463
CECS 463System On ChipChapter 2 MATLABDigital Signal Processing Using MATLAB and Wavelets, M.Weeks, Infinity Science Press, 2007, pp. 29-841MATLAB BasicsScalars (or constants): a=3.5 or b=piVectors (row or column): c=[1 2] ord=[3;4]Matrices: A =
CSU Long Beach - CECS - 463
CECS 463System On ChipChapter 3 FiltersDigital Signal Processing Using MATLAB and Wavelets, M.Weeks, Infinity Science Press, 2007, pp. 85-1321FiltersComponentsExample: Let a=[1,2,3,4], b=[2,1,2,1] asinputsnth output sample isc(n)=0.5a(n)-0.5b(n
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The Discrete FourierTransformPeriodically SampledSignalsThe DFTThe DFT:N 1X (m) = x(n) e j wN n m for m = 0,1,.N 1n =0where wN = 2/NSample vector x has length NSequence x(n) is periodic of period N sothat sampled signal x(nkN) = x(n) for anyk
CSU Long Beach - CECS - 529
CECS 429/529 Exam 2, Fall 2010, Dr. Ebert1a. Consider the following table which indicates how often a term occurs within a given document.archerybaseballcyclingdodgeballDoc1 Doc2 Doc3 Doc400600083000451000Express each document as a
CSU Long Beach - CECS - 529
CECS 429/529 Practice Final Exam, Fall 2010, Dr. Ebert1. When intersecting the postings lists of more than two terms, a common heuristic is to select thelists to intersect in terms of increasing size. For example, for three terms whose list sizes are 20
CSU Long Beach - CECS - 529
CECS 429/529 Quiz 1, Fall 2010, Dr. Ebert1. Given the documents Doc 1. Locate apple in the dictionary. Doc 2. Retrieve its postings. Doc 3. Locate banana in the dictionary.Provide the term-document incidence matrix for this document collection. (10 p
CSU Long Beach - CECS - 529
CECS 429/529 Quiz 2, Fall 2010, Dr. Ebert1. Generally speaking, what eect does stemming have on the precision and recall of a booleanquery? Explain. (10 points)2. Give an example of two words that share the same root (i.e. stem), but whose meanings are
CSU Long Beach - CECS - 529
CECS 429/529 Quiz 3, Fall 2010, Dr. EbertDirections. Complete this quiz in one sitting, and in time not exceeding one hour. You may useyour textbook and class notes, but no other resources. You are not allowed to communicate withanyone except the instr