ࡱ> wyv{|}3 SVW bjbjcTcT .>>T'?44ww###8[#qtHFFF8p:p:p:p:p:p:p$r/up^puFBFFF^pwwgpFwl8pF8pJ6c\,*j#eB$pp0qeVu<u*j*jun`FFFFFFF^p^pFFFqFFFFuFFFFFFFFF4 =: Chapter 13: Comparing Two Population Parameters Objectives: Students will: Identify the conditions that need to be satisfied in order to do inference for comparing two population means. Construct a confidence interval for the difference between two population means. Perform a significance test for the difference between two population means. Identify the conditions that need to be satisfied in order to do inference for comparing two population proportions. Construct a confidence interval for the difference between two population proportions. Perform a significance test for the difference between two population proportions. AP Outline Fit: IV. Statistical Inference: Estimating population parameters and testing hypotheses (30%40%) A. Estimation (point estimators and confidence intervals) 5. Large sample confidence interval for a difference between two proportions 7. Confidence interval for a difference between two means B. Tests of significance 3. Large sample test for a difference between two proportions 5. Test for a difference between two means What you will learn: Recognition Determine whether a problem requires inference about comparing means or proportions. Recognize from the design of a study whether one-sample t, paired t, or two-sample t procedures are needed. Two-Sample t Procedures Calculate and interpret a confidence interval for the difference between two means. Use the two-sample t statistic with conservative degrees of freedom if you do not have statistical software. Use the TI-83/84/89 or software if you have it. Test the hypothesis that two populations have equal means against either a one-sided or a two-sided alternative. Use the two-sample t test with conservative degrees of freedom if you do not have statistical software. Use the TI-83/84/89 or software if you have it. Recognize when the two-sample t procedures are appropriate in practice. Comparing Two Proportions Use the two-sample z procedure to give a confidence interval for the difference  QUOTE   between proportions in two populations based on independent SRSs from the populations. Use a two-proportion z test to test the hypothesis  QUOTE   that proportions in two distinct populations are equal. Check that you can safely use these z procedures in a particular setting. Section 13.1: Comparing Two Means Knowledge Objectives: Students will: Describe the three conditions necessary for doing inference involving two population means. Clarify the difference between the two-sample z statistic and the two-sample t statistic. Construction Objectives: Students will be able to: Identify situations in which two-sample problems might arise. Identify the two practical options for using two-sample t procedures and how they differ in terms of computing the number of degrees of freedom. Conduct a two-sample significance test for the difference between two independent means using the Inference Toolbox. Compare the robustness of two-sample procedures with that of one-sample procedures. Include in your comparison the role of equal sample sizes. Explain what is meant by pooled two-sample t procedures, when pooling can be justified, and why it is advisable not to pool. Vocabulary: Statistics Key Concepts:  EMBED PowerPoint.Slide.12  2 Sample t-Test: Degrees of Freedom: Since we dont know the standard deviations we use the t-distribution for our test statistic. But we have a problem with calculating the degrees of freedom! We have two options: Let our calculator handle the complex calculations and tell us what the degrees of freedom are Use the smaller of n1 1 and n2 1 as a conservative estimate of the degrees of freedom  EMBED PowerPoint.Slide.12   EMBED PowerPoint.Slide.12  Example 1: Does increasing the amount of calcium in our diet reduce blood pressure? Subjects in the experiment were 21 healthy black men. A randomly chosen group of 10 received a calcium supplement for 12 weeks. The control group of 11 men received a placebo pill that looked identical. The response variable is the decrease in systolic (top #) blood pressure for a subject after 12 weeks, in millimeters of mercury. An increase appears as a negative response. Data summarized below Subjects 1234567891011Calcium 7-41817-3-511011-2----Control -112-1-33-552-11-1-3 Calculate the summary statistics. Test the claim Step 1: Hypothesis H0: Ha: Step 2: Conditions SRS: Normality: Independence: Step 3: Calculations Test Statistic: Step 4: Interpretation Example 2: The following data collected from two independently done simple random samples on average cell phone costs: DataProvider 1Provider 2n2313x-bar43.141.0s4.55.1Test the claim that 1 > 2 at the  = 0.05 level of significance Step 1: Hypothesis H0: Ha: Step 2: Conditions SRS: Normality: Independence: Step 3: Calculations Test Statistic: Step 4: Interpretation Construct a 95% confidence interval about 1 - 2 Homework: pg 791: 13.7, 13.8, 13.11 and pg 804 13.17, 13.18, 13.23, 13.24 Section 13.2: Comparing Two Proportions Knowledge Objectives: Students will: Identify the mean and standard deviation of the sampling distribution of  QUOTE  1  QUOTE  2. List the conditions under which the sampling distribution of  QUOTE  1  QUOTE  2 is approximately Normal. Identify the standard error of  QUOTE  1  QUOTE  2 when constructing a confidence interval for the difference between two population proportions. Identify the three conditions under which it is appropriate to construct a confidence interval for the difference between two population proportions. Explain why, in a significance test for the difference between two proportions, it is reasonable to combine (pool) your sample estimates to make a single estimate of the difference between the proportions. Explain how the standard error of  QUOTE  1  QUOTE  2 differs between constructing a confidence interval for  QUOTE  1  QUOTE  2 and performing a hypothesis test for  QUOTE  . List the three conditions that need to be satisfied in order to do a significance test for the difference between two proportions. Construction Objectives: Students will be able to: Construct a confidence interval for the difference between two population proportions using the four-step Inference Toolbox for confidence intervals. Conduct a significance test for the difference between two proportions using the Inference Toolbox. Vocabulary: Combined sample proportion Key Concepts:  EMBED PowerPoint.Slide.12   EMBED PowerPoint.Slide.12  Example 1: A study of the effect of pre-school had on later use of social services revealed the following data. PopulationDescriptionSample SizeSocial ServiceProportion1Control61490.8032Preschool62380.613Compute a 95% confidence interval on the difference between the control and Pre-school group proportions Conditions: SRS Normality Independence Calculations: Conclusion: Example 2: We have two independent samples. 55 out of a random sample of 100 students at one university are commuters. 80 out of another random sample of 200 students at different university are commuters. We wish to know of these two proportions are equal. We use a level of significance  = .05 Step 1: Hypothesis H0: Ha: Step 2: Conditions SRS: Normality: Independence: Step 3: Calculations Test Statistic: Step 4: Interpretation Example 3: A sports medicine researcher for a university wishes to estimate the difference between the proportion of male athletes and female athletes who consume the USDAs recommended daily intake of calcium. What sample size should he use if he wants to estimate to be within 3% at a 95% confidence level? if he uses a 1994 study as a prior estimate that found 51.1% of males and 75.2% of females consumed the recommended amount if he does not use any prior estimates Homework: pg 819 13.29, 13.30 and pg 821 13.33-35, 13.38 Chapter 13: Review Objectives: Students will be able to: Summarize the chapter Define the vocabulary used Know and be able to discuss all sectional knowledge objectives Complete all sectional construction objectives Successfully answer any of the review exercises Identify the conditions that need to be satisfied in order to do inference for comparing two population means. Construct a confidence interval for the difference between two population means. Perform a significance test for the difference between two population means. Identify the conditions that need to be satisfied in order to do inference for comparing two population proportions. 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X@,UwX. ,$Gy=y=&ewpdv%    Tn oq L`Two Means>^GcAAGA% ( " " FEMF+*@$??`%CpA*@$??`%CpA*@$99*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$??`%CpA*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??ztD"D*@$??ztD"D*@$??ztD"D*@$??ztD"D*@$??ztD"D*@$99*@$??ztD"D*@$??ztD"D*@$??ztD"D@ !!K@0   # ??ztD"D$$??ztD"D  Rp"Arial,l,A0_঱ 4DB,$G,,8`,w)!;oqζ ,́w)!;oqhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w . @,Uw. ,$Gy=y=&ewpdv%    I}TlILlTest Statistic:(**2***% ( " " FEMF+*@$??ztD"D*@$??ztD"D*@$99*@$??ztD"D*@$??ztD"D*@$??ztD"D*@$??ztD"D*@$??ztD"D*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99@th >K J>K_J9KJJ_JJJ|JS J\Je4 JJKq, J3<Kw J>K J?@( !b $$>>'%  % VDg F  0Z0Z=iV=S==SzTKUOWX0Z%  % $$AAF`TEMF+@@4F?@$$>>_888% %  ;1ZX(7Z=Z=Z6=Z=X4=Z@;ZC9ZF6ZH3ZI0ZIY$iV(=SIX4:SI7SH4SF2SC0S@0S=60SX40S2S6S9S>SASY0~T?|T?U}PWX=XY(MWUwTWX(wTWvTWuTWY@ 9SISIS=F?@`J]JJr JJ U JJDJ-JhCJ}JJI0J3IJIA JIIcJIIbJII6yJIJ*IPJIJRJgJDJJnF J@K JLKK J@( $$>>_888% '%  ;?Y4???@H@u@@@AA'BBCiDXDDD.\EEE FWFFF_G2OGGGeDHHjHaI>|IIIIIGI -J`JJ}JJi)K\KhvK-K K K Kd K; L 1L OL X(PL RL TL 6nL X(pL rL tL 6L X(L L L 6L X(L L L 6L X(L L L 6L X(L L M 6M X(M M "M Y=M [M yM8 Ma M M M N+(NebNNfNOzHOOO ODO} P(PCP^P;PP%QhQQf:RmRR4RaSbSSS\TT+.U@URVa WxWWmXXAYYYZ=Z4ZZYYoE\EwDDCB-BAFA@z@N@$@??? ? =<?I  % % $$AA( F|pEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99@@4>F?@, `JJ0KhJ@$$>>_888% %  V,F ?!&Z$&Zo?l % % $$AA( " FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$99*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD@ !!K@0   # ??A%EvAD$$??A%EvAD  Rp"Arial,l,A0_঱  BB,$G,,??FAILwP)!;)!;hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. @,Uw. ,$G9wJw&ewpdv%    TTT f L9LPt% ( " " FdXEMF+*@$??A%EvAD*@$??A%EvAD@ !!K@0   # ??A%EvAD$$??A%EvAD  Rp"Arial,l,A0_঱ T AB@B,$G,,8`,w)!;98|D,́w)!;9hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    TTg )~ UGLP% ( " " FEMF+*@$??A%EvAD*@$??A%EvAD*@$99*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$??A%EvAD*@$99*@$99+@ *@$99*@$99@@4>F?@, JX< JJxJ@!b $$>>_888% %  V,_ k NS`NSSS` % % $$AA( FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99@th /J J/J4FJCJf-JJ4FJJ0J.J JJ JJ Jo*J J/J J?@( $$=='%  % VD| w/wq0oh0iq0i-El.n /q^/t/w/%  % $$AAF`TEMF+@ @4F?@ $$==_888% %  ;w/X(w/w/w/6wq0X4ww0w~0w0w0w0w0Y$o0i0X4i0i0i0i~0iw0iq06i-X4i-i-i-i-i-i-Y0Nlv.Jlu.n.qE/uo/=t/Y(qw/n#/Al.X(?l.>l.=l.Y@ i-i-iq0iX0oO0wX0wq0w/w/=<?~  % % $$AA( FxEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99@ th lFJE JlFJd-J\J8JpJd-JpJ`JhJ J`J JWJ J6NJv JlFJE J?@ $$==%  % VD+   B/Bh0(J0Ph0P-)N.K/HU/pE/B/%  % $$AAF`TEMF+@ @4F?@  $$==_888% %  ;B/Y@ B/Bh0BO0)J0PO0Ph0P-P-2N.X(1N./N..N.Y(K/Hn/qE/=nEf/Y0|H=/K.%Nm. Nn.P|-X4Py-Pz-P-P-P-P-6Ph0X(Pv0P0P0Y$'J0B0X(B0Bv0Bh06B/X(B/B/B/=<?)   % % $$AA( " FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$99*@$??UD[?D*@$??UD[?D*@$??UD[?D@ !!K@0   # ??UD[?D$$??UD[?D  Rp"Arial,l,A0_঱ / BB,$G,,??FAILwP)!;)!;hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wT. @,Uw. ,$G9wJw&ewpdv%    TT E9LP-% ( " " FdXEMF+*@$??UD[?D*@$??UD[?D@ !!K@0   # ??UD[?D$$??UD[?D  Rp"Arial,l,A0_঱ 8ۛBB,$G,,8`,w)!;9\ $I,́w)!;9hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    TT E9LPt% ( " " FdXEMF+*@$??UD[?D*@$??UD[?D@ !!K@0   # ??UD[?D$$??UD[?D  Rp"Arial,l,A0_঱ ܛpAAB@B,$G,,8`,w)!;9\ x,́w)!;9hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    TT"5N&GLP% ( " " FdXEMF+*@$??UD[?D*@$??UD[?D@ !!K@0   # ??UD[?D$$??UD[?D  Rp"Arial,l,A0_঱ ޛBAB@B,$G,,8`,w)!;&G{r,́w)!;&Ghw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w\. X@,UwX. ,$Gy=y=&ewpdv%    TX6"VN>GLP/2 % ( " " FEMF+*@$??UD[?D*@$??UD[?D*@$99*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$??UD[?D*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$99*@$??DX@D*@$??DX@D*@$??DX@D@ !!K@0   # ??DX@D$$??DX@D  Rp"Arial,l,A0_঱ 4N BB,$G,,8`,w)!;>Gt 8# ,́w)!;>Ghw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. @,Uw. ,$Gy=y=&ewpdv%    TTJ9LPt% ( " " FdXEMF+*@$??DX@D*@$??DX@D@ !!K@0   # ??DX@D$$??DX@D  Rp"Arial,l,A0_঱ AB@B,$G,,8`,w)!;9lF4y,́w)!;9hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    TT'SGLP=% ( " " FdXEMF+*@$??DX@D*@$??DX@D@ !!K@0   # ??DX@D$$??DX@D  Rp"Arial,l,A0_঱ &AAB@B,$G,,8`,w)!;G, 0 ,́w)!;Ghw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    TX'S+GLP/2 % ( " " FpdEMF+*@$??DX@D*@$??DX@D*@$99*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$??DX@D*@$99*@$99+@ *@$99*@$99@ @4>F?@  FJVJrxLJk JjbJM JlJ`JvJ =JF?@, 8gJ J8gJ J@$$==_888% %  V,j.jI1piI1pi. % % $$AA( F|pEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99@@4>F?@, pJ JpJOJ@$$==_888% %  V,P[.P 1WP 1WP[. % % $$AA( FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99@th >_HJ>_HJ IJpWIJpWIЅJw:I'U JI9 JgeHE JHK=J>_HJ?@( $$=='%  % VDJ!  /0 0 0 -.' E/1 /C//%  % $$AAF`TEMF+@@4F?@$$==_888% %  ;/Y@ /00 0 00--.X(...Y(, ]/4 /E/=B/Y0. /# ,/..-X4----"-"-6"0X4"0 0000 0Y$ 00X40000006/X(///=<?G$ % % $$AA( " FXLEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$99*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD@ !!K@0   # ??ZCXBD$$??ZCXBD  Rp"Arial,l,A0_঱ T=N BB,$G,,??FAILP/)!;)!;hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w.. L@,UwL. ,$G9wJw&ewpdv%    TT#P9LP-/% ( " " FdXEMF+*@$??ZCXBD*@$??ZCXBD@ !!K@0   # ??ZCXBD$$??ZCXBD  Rp"Arial,l,A0_঱ BB,$G,,8`,w)!;9  ,́w)!;9hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w4. X@,UwX. ,$Gy=y=&ewpdv%    TT$6P9LPt% ( " " FdXEMF+*@$??ZCXBD*@$??ZCXBD@ !!K@0   # ??ZCXBD$$??ZCXBD  Rp"Arial,l,A0_঱ pAAB@B,$G,,8`,w)!;9P (\ ,́w)!;9hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w7. X@,UwX. ,$Gy=y=&ewpdv%    TT7-NY&GLP% ( " " FEMF+*@$??ZCXBD*@$??ZCXBD*@$99*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$??ZCXBD*@$99*@$99+@ *@$99*@$99@@4>F?@, pWI~ JpWI8J@( !b $$==_888% '%  V,' T,/T11,/ % % $$AA( FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99@@4>F?@}WHVJ4Hk J))IM JYPI`JwI =JI|?IjI*I6ܝIIIIIIII5bIIIQII>I] III]>_888% %  [X  5ziVzYVYVzVzV55zViVVV % % $$AA( Fl`EMF+*@$99+@ *@$99*@$99@"pFFA?X@ A?`@#4(&*JP/JBJP/JBJ`-J@#"$$==_888% %  [X  k:o:o;o1p1p7;k7;k:o1oh0p1o1 % % $$AA( " FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$99*@$??UnD2C*@$??UnD2C*@$??UnD2C@ !!K@0   # ??UnD2C$$??UnD2C  RpTimes New RomanBBB,$G,,??FAILwP)!;hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w\. @,Uw. ,$G9wJw&ewpdv%    TT'Ol@LPP)% ( " " FdXEMF+*@$??UnD2C*@$??UnD2C@ !!K@0   # ??UnD2C$$??UnD2C  RpTimes New RomanBBB,$G,,8`,w)!;l@  ,́w)!;l@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wa. X@,UwX. ,$Gy=y=&ewpdv%    TTPe@LP-% ( " " FdXEMF+*@$??UnD2C*@$??UnD2C@ !!K@0   # ??UnD2C$$??UnD2C  RpTimes New RomanC^DB,$G,,8`,w)!;@  ,́w)!;@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,we. X@,UwX. ,$Gy=y=&ewpdv%    Tf@LValue is the area highlighted*"%%""%"%"%%% ( " " FH<EMF+*@$??UnD2C*@$??UnD2C*@$99*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$??UnD2C*@$99*@$99+@ *@$99*@$99@$pFFA?X@ A?`@%<0 ,J"I0NI"I0NI8JMI8J@%$!b $$==_888% %  [X 9 J k g,$,) 9 9 l,1-S,l, % % $$AA( FtEMF+*@$99+@ *@$99*@$99@&pFFA?X@ A?`@'H<JKIJI8JI8J8JkJ8J@'&$$==_888% %  [p]]==d=-=-M-M.=.=B]B]d]]M'-4O-M.M'- % % $$AA( FthEMF+*@$99+@ *@$99*@$99@(pFFA?X@ A?`@)<0J"IJ"IJ8JZJ8J@)($$>>_888% %  [X  @TSVSVSS@@QTLSSQTL % % $$AA( FtEMF+*@$99+@ *@$99*@$99@*pFFA?X@ A?` @+H<JKIJI)JI)J8J~J8J@+*$$==_888% %  [p]]d]B|B|.l.l-b|-A|-A|db|]]]^l.j-^l'-^l. % % $$AA( " FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$99*@$??@DD*@$??@DD*@$??@DD@ !!K@0   # ??@DD$$??@DD  Rp"Arial,l,A0_঱ қ`BB,$G,,??FAILP)!;hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wu. @,Uw. ,$G9wJw&ewpdv%    TX@z1LP|t% ( " " FdXEMF+*@$??@DD*@$??@DD@ !!K@0   # ??@DD$$??@DD  Rp"Arial,l,A0_঱ 8ߛ0AAhB$B,$G,,8`,w)!;1 ( ,́w)!;1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w{. X@,UwX. ,$Gy=y=&ewpdv%    TT\=LP0% ( " " FdXEMF+*@$??@DD*@$??@DD@ !!K@0   # ??@DD$$??@DD  Rp"Arial,l,A0_঱ 8ܛA`BB,$G,,8`,w)!;=  ,́w)!;=hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w~. X@,UwX. ,$Gy=y=&ewpdv%    TT@z11LP|% ( " " FEMF+*@$??@DD*@$??@DD*@$99*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$??@DD*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$99*@$??U)DD*@$??U)DD*@$??U)DD@ !!K@0   # ??U)DD$$??U)DD  Rp"Arial,l,A0_঱ 8;N `BB,$G,,8`,w)!;11  ,́w)!;11hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. @,Uw. ,$Gy=y=&ewpdv%    TTq@z1LP-% ( " " FdXEMF+*@$??U)DD*@$??U)DD@ !!K@0   # ??U)DD$$??U)DD  Rp"Arial,l,A0_঱ P`BB,$G,,8`,w)!;1H D ,́w)!;1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    TX@z1LP|t% ( " " FdXEMF+*@$??U)DD*@$??U)DD@ !!K@0   # ??U)DD$$??U)DD  Rp"Arial,l,A0_঱ ?N AAhB$B,$G,,8`,w)!;1T ) ,́w)!;1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w4. X@,UwX. ,$Gy=y=&ewpdv%    TT\0=LP0% ( " " FdXEMF+*@$??U)DD*@$??U)DD@ !!K@0   # ??U)DD$$??U)DD  Rp"Arial,l,A0_঱ ~ B`BB,$G,,8`,w)!;0=@ P ,́w)!;0=hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wx. X@,UwX. ,$Gy=y=&ewpdv%    TT@zB1LP|% ( " " FEMF+*@$??U)DD*@$??U)DD*@$99*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$??U)DD*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$99*@$??CXD*@$??CXD*@$??CXD@ !!K@0   # ??CXD$$??CXD  Rp"Arial,l,A0_঱ ~ `BB,$G,,8`,w)!;B1x t ,́w)!;B1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. @,Uw. ,$Gy=y=&ewpdv%    TTA{1LPt% ( " " FdXEMF+*@$??CXD*@$??CXD@ !!K@0   # ??CXD$$??CXD  Rp"Arial,l,A0_঱ 8| @AhB$B,$G,,8`,w)!;1  ,́w)!;1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wP. X@,UwX. ,$Gy=y=&ewpdv%    TT]=LP0% ( " " F$EMF+*@$??CXD*@$??CXD*@$99*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$??CXD*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$99*@$??n*EXD*@$??n*EXD*@$??n*EXD@ !!K@0   # ??n*EXD$$??n*EXD  Rp"Arial,l,A0_঱ T `BB,$G,,8`,w)!;=  ,́w)!;=hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. @,Uw. ,$Gy=y=&ewpdv%    TT A {1LPt% ( " " FdXEMF+*@$??n*EXD*@$??n*EXD@ !!K@0   # ??n*EXD$$??n*EXD  Rp"Arial,l,A0_঱ @AhB$B,$G,,8`,w)!;1  ,́w)!;1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    TT ] =LP0% ( " " FEMF+*@$??n*EXD*@$??n*EXD*@$99*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$??n*EXD*@$99*@$99+@ *@$99*@$99*@$99UDDD@,@4pFF?@-, ZI 1IZIpJ@-,!b $$>>_888% %  V,%L6%D%D%L6 % % $$AA( FEMF+@.@4pFF?@/, J 1IJpJ@/.$$>>_888% %  V,elR3L6R3D13D13L6 % % $$AA( FEMF+@0@4pFF?@1, <_H .JH@10$$>>_888% %  V, PWk2NE2NE2k2 % % $$AA( FEMF+@2@4pFF?@3, <_2I .J2I@32$$>>_888% %  V, kL6NEL6NEm6km6 % % $$AA( FEMF+@4@4pFF?@5, <_I .JI@54$$>>_888% %  V, @Gk :NE :NE-:k-: % % $$AA( FEMF+@6@4>F?@7, <_pJ@76$$>>_888% %  V, .DkDk. % % $$AA( FEMF+@8@4>F?@9, lJ<_lJpJ@98$$>>_888% %  V,NE.NEDEDE. % % $$AA( FEMF+@:@4>F?@;, <_ .J@;:$$>>_888% %  V, k.NE.NE/k/ % % $$AA( FEMF+@<@4>F?@=, <_4J .J4J@=<$$>>_888% %  V, k]DNE]DNEDkD % % $$AA( " FEMF+*@$99*@$99+@ *@$99*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New RomanuC@[DB,$G,l,!;=8  8`,w)!;=  hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. ,Uw. ,$G9wJw&ewpdv%    TSkB"HLReject null hypothesis, if6!!!)))&)%)!% ( " " FEMF+*@$??*LD`D*@$??*LD`D*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$99*@$99+@ *@$99*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New RomanCCB,$G,l,88,w)!;"HL  ,́w)!;"Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. ,Uw. ,$Gy=y=&ewpdv%    TT'fTHLPP.% ( " " FdXEMF+*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New RomanCBB,$G,l,88,w)!;H$ ( ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wT. X,UwX. ,$Gy=y=&ewpdv%    TTUfm$HLP-% ( " " FdXEMF+*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New RomanDCB,$G,l,88,w)!;$H0 H ,́w)!;$Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    T|nfg=HL\value < %%)!+% ( " " FdXEMF+*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New RomanBDCB,$G,l,88,w)!;=H ධ ,́w)!;=Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TThf7HLP*% ( " " FxEMF+*@$??*LD`D*@$??*LD`D*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$99*@$99+@ *@$99*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New Roman$_CB,$G,l,88,w)!;7H` P ,́w)!;7Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wH. x,Uwx. ,$Gy=y=&ewpdv%    Td52HLTLeft2!% ( " " FdXEMF+*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New RomanBBB,$G,l,88,w)!;H`F  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TT2HLP-% ( " " FdXEMF+*@$??*LD`D*@$??*LD`D@ !!K@0   # ??*LD`D$$??*LD`D  RpTimes New RomanBCB,$G,l,88,w)!;H  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    Tp2HLXTailed+%!)% ( " " F<0EMF+*@$??*LD`D*@$??*LD`D*@$99*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$??*LD`D*@$99*@$99+@ *@$99*@$99*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$99*@$??D`D*@$??D`D*@$??D`D@ !!K@0   # ??D`D$$??D`D  RpTimes New RomancCB,$G,l,88,w)!;H_ k ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w`. 0,Uw0. ,$Gy=y=&ewpdv%    T`f2HLTTwo,8%% ( " " FdXEMF+*@$??D`D*@$??D`D@ !!K@0   # ??D`D$$??D`D  RpTimes New RomanBBB,$G,l,88,w)!;HF 0_ ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TTg2HLP-% ( " " FdXEMF+*@$??D`D*@$??D`D@ !!K@0   # ??D`D$$??D`D  RpTimes New RomanBCB,$G,l,88,w)!;H  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TpC2HLXTailed+%!)% ( " " F<0EMF+*@$??D`D*@$??D`D*@$99*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$99*@$99+@ *@$99*@$99*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$99*@$??D`D*@$??D`D*@$??D`D@ !!K@0   # ??D`D$$??D`D  RpTimes New Roman0ACB,$G,l,88,w)!;IT,8w0I@@,́w)!;,URv,RvIxRvK@@@`0_d,,Tv=xRv,OwGDIC@,w,. 0,Uw0. ,$Gy=y=&ewpdv%    Tlq28HLXRightq06&)% ( " " FdXEMF+*@$??D`D*@$??D`D@ !!K@0   # ??D`D$$??D`D  RpTimes New Roman>CBB,$G,l,88,w)!;8H@_ o ,́w)!;8Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w`. X,UwX. ,$Gy=y=&ewpdv%    TTr2HLP-=% ( " " FdXEMF+*@$??D`D*@$??D`D@ !!K@0   # ??D`D$$??D`D  RpTimes New RomanWCCB,$G,l,88,w)!;H  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TpN2HLXTailed+%!)% ( " " FEMF+*@$??D`D*@$??D`D*@$99*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$??D`D*@$99*@$99+@ *@$99*@$99*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$99*@$??*LDD*@$??*LDD*@$??*LDD@ !!K@0   # ??*LDD$$??*LDD  RpTimes New RomanABB,$G,l,88,w)!;HL_ o ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. ,Uw. ,$Gy=y=&ewpdv%    TTuDHLPt9% ( " " FdXEMF+*@$??*LDD*@$??*LDD@ !!K@0   # ??*LDD$$??*LDD  RpTimes New Roman|BAB|B,$G,l,88,w)!;DH0 D ,́w)!;DHhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TT!]ZLP09% ( " " FdXEMF+*@$??*LDD*@$??*LDD@ !!K@0   # ??*LDD$$??*LDD  RpTimes New RomanBCB,$G,l,88,w)!;]Zl L ,́w)!;]Zhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w<. X,UwX. ,$Gy=y=&ewpdv%    TXHLP< +% ( " " FdXEMF+*@$??*LDD*@$??*LDD@ !!K@0   # ??*LDD$$??*LDD  RpTimes New RomanCBB,$G,l,88,w)!;Hh F ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TTHLP-D% ( " " FdXEMF+*@$??*LDD*@$??*LDD@ !!K@0   # ??*LDD$$??*LDD  RpTimes New RomanDCBB,$G,l,88,w)!;H t ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w . X,UwX. ,$Gy=y=&ewpdv%    TT":HLPt% ( " " FdXEMF+*@$??*LDD*@$??*LDD@ !!K@0   # ??*LDD$$??*LDD  RpTimes New RomanlCAB|B,$G,l,88,w)!;H  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w . X,UwX. ,$Gy=y=&ewpdv%    TT;V! ZLP% ( " " FthEMF+*@$??*LDD*@$??*LDD*@$99*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$??*LDD*@$99*@$99+@ *@$99*@$99*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DmD*@$??DD*@$??DD*@$??DD*@$??DmD*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DvE*@$??DmD*@$99*@$??DmD*@$??DmD*@$??DmD@ !!K@0   # ??DmD$$??DmD  RpTimes New RomanABB,$G,l,88,w)!; Z  ,́w)!; Zhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wP. h,Uwh. ,$Gy=y=&ewpdv%    TT f%5HLPt% ( " " FdXEMF+*@$??DmD*@$??DmD@ !!K@0   # ??DmD$$??DmD  RpTimes New Roman@BAB|B,$G,l,88,w)!;5H  ,́w)!;5Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TT&>NZLP0 ,% ( " " FdXEMF+*@$??DmD*@$??DmD@ !!K@0   # ??DmD$$??DmD  RpTimes New RomanBCB,$G,l,88,w)!;NZ  ,́w)!;NZhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X,UwX. ,$Gy=y=&ewpdv%    TXQfyHLP< +% ( " " FdXEMF+*@$??DmD*@$??DmD@ !!K@0   # ??DmD$$??DmD  RpTimes New Roman CBB,$G,l,88,w)!;yH F ,́w)!;yHhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w0#. X,UwX. ,$Gy=y=&ewpdv%    TTfHLP-9% ( " " FdXEMF+*@$??DmD*@$??DmD@ !!K@0   # ??DmD$$??DmD  RpTimes New Roman5CBB,$G,l,88,w)!;H  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wt&. X,UwX. ,$Gy=y=&ewpdv%    TTfHLPt% ( " " FdXEMF+*@$??DmD*@$??DmD@ !!K@0   # ??DmD$$??DmD  RpTimes New Roman]CAB|B,$G,l,88,w)!;H0 ( ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w). X,UwX. ,$Gy=y=&ewpdv%    TTZLP% ( " " FdXEMF+*@$??DmD*@$??DmD@ !!K@0   # ??DmD$$??DmD  RpTimes New RomanyCAB|B,$G,l,88,w)!;ZX H ,́w)!;Zhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w,. X,UwX. ,$Gy=y=&ewpdv%    TXZLP/2% ( " " FEMF+*@$??DmD*@$??DmD*@$??DD*@$??DD@ !!K@0   # ??DD$$??DD  RpTimes New RomanB CB,$G,l,88,w)!;Z F ,́w)!;Zhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wD0. ,Uw. ,$Gy=y=&ewpdv%    TXnHLPor%!% ( " " FEMF+*@$??DD*@$??DmD*@$??DvE*@$??DvE@ !!K@0   # ??DvE$$??DvE  RpTimes New RomanABB,$G,l,88,w)!;H F ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w3. ,Uw. ,$Gy=y=&ewpdv%    TT1nAHLPt% ( " " FdXEMF+*@$??DvE*@$??DvE@ !!K@0   # ??DvE$$??DvE  RpTimes New RomanpBAB|B,$G,l,88,w)!;AH  ,́w)!;AHhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w`7. X,UwX. ,$Gy=y=&ewpdv%    TT2CJ{ZZLP0% ( " " FdXEMF+*@$??DvE*@$??DvE@ !!K@0   # ??DvE$$??DvE  RpTimes New RomanBCCB,$G,l,88,w)!;ZZ  ,́w)!;ZZhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w:. X,UwX. ,$Gy=y=&ewpdv%    Td]nHLT> t+% ( " " FdXEMF+*@$??DvE*@$??DvE@ !!K@0   # ??DvE$$??DvE  RpTimes New RomanPCAB|B,$G,l,88,w)!;HF  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w=. X,UwX. ,$Gy=y=&ewpdv%    TTC{ZLP% ( " " FdXEMF+*@$??DvE*@$??DvE@ !!K@0   # ??DvE$$??DvE  RpTimes New RomanlCAB|B,$G,l,88,w)!;Z$  ,́w)!;Zhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w t+% ( " " FdXEMF+*@$??DD*@$??DD@ !!K@0   # ??DD$$??DD  RpTimes New RomanCAB|B,$G,l,88,w)!;HF  ,́w)!;Hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wU. X,UwX. ,$Gy=y=&ewpdv%    TT!IZLP% ( " " FEMF+*@$??DD*@$??DD*@$99*@$??DD*@$??DD*@$??DD*@$??DD*@$??DD*@$??DD*@$??DD*@$??DD*@$??DD*@$??DD*@$??DD*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$99*@$??pDC*@$??pDC*@$??pDC@ !!K@0   # ??pDC$$??pDC  Rp"Arial,l,A0_঱ 0HDtB,$G,, | ,́w)!;IZ | )!;DTimehw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w$Y. @,Uw. ,$Gy=y=&ewpdv%    T$,P)$LRemember to add the areas in the two%%       !% ( " " FdXEMF+*@$??pDC*@$??pDC@ !!K@0   # ??pDC$$??pDC  Rp"Arial,l,A0_঱ T @5D0BtB,$G,,8`,w)!;)P\$ ,́w)!;)hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wa. X@,UwX. ,$Gy=y=&ewpdv%    TTP')LP-% ( " " FdXEMF+*@$??pDC*@$??pDC@ !!K@0   # ??pDC$$??pDC  Rp"Arial,l,A0_঱ 8 8D0.CtB,$G,,8`,w)!;)  ,́w)!;)hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,we. X@,UwX. ,$Gy=y=&ewpdv%    Tx(P)L\tailed!a % ( " " F, EMF+*@$??pDC*@$??pDC*@$99*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$??pDC*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD*@$99*@$??@DUD*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ ? C CB,$G,,8`,w)!;)C  ,́w)!;)hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w|h. @,Uw . ,$Gy=y=&ewpdv%    I}TX#p@LP(x%% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ \CAB`B,$G,,8`,w)!;@, G ,́w)!;@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wy. X@,UwX. ,$Gy=y=&ewpdv%    I}TTI{PLP1% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱  yCBB,$G,,8`,w)!;I|,8w0I@@,́w)!;,URv,RvIxRvK@@@`0_,,Tv=xRv,OwGDIC@,w|. X@,UwX. ,$Gy=y=&ewpdv%    I}TT#?p!@LP %% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ T CBB,$G,,8`,w)!;!@8 < ,́w)!;!@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TTS#wpY@LPx?%% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ CAB`B,$G,,8`,w)!;Y@P H ,́w)!;Y@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wX. X@,UwX. ,$Gy=y=&ewpdv%    I}TTxI{~PLP2% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ CBB,$G,,8`,w)!;~PX T ,́w)!;~Phw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TX#p@LP) % ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱  CBB,$G,,8`,w)!;@\ (G ,́w)!;@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TT#p@LP %% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ CBB,$G,,8`,w)!;@p h ,́w)!;@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w(. X@,UwX. ,$Gy=y=&ewpdv%    I}TT#p@LP(% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  RpTimes New RomanCBB,$G,,8`,w)!;@| t ,́w)!;@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wl. X@,UwX. ,$Gy=y=&ewpdv%    I}TT$,o @LP&% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱  @DAB`B,$G,,8`,w)!; @  ,́w)!; @hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TX-IR{3PLP1 % ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ @ DBB,$G,,8`,w)!;3P G ,́w)!;3Phw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TTS#wpY@LP w%% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  RpTimes New RomanDBB,$G,,8`,w)!;Y@  ,́w)!;Y@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w<. X@,UwX. ,$Gy=y=&ewpdv%    I}TT$o@LPw&% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ 8 'DAB`B,$G,,8`,w)!;@  ,́w)!;@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TTI{PLP2% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ .DBB,$G,,8`,w)!;P  ,́w)!;Phw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wĠ. X@,UwX. ,$Gy=y=&ewpdv%    I}TX# p@LP) % ( " " FEMF+*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ Բ BB,$G,,8`,w)!;@ G ,́w)!;@hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w . @,Uw. ,$Gy=y=&ewpdv%    I}TTtALPt% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱  AB\B,$G,,8`,w)!;A  ,́w)!;Ahw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TT'QLP0% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ A CB,$G,,8`,w)!;Q  ,́w)!;Qhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wܪ. X@,UwX. ,$Gy=y=&ewpdv%    I}TX;tsAALP= '% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ B@DB,$G,,8`,w)!;AA ύ ,́w)!;AAhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w$. X@,UwX. ,$Gy=y=&ewpdv%    I}Ttt& zAL-------------------------------% ( " " FEMF+*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ < CBB,$G,,8`,w)!;zA@ C ,́w)!;zAhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. @,Uw. ,$Gy=y=&ewpdv%    I}TT%I+1LPs%% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ T; CAB\B,$G,,8`,w)!;+1  ,́w)!;+1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TTJa PALP1% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ 87 CBB,$G,,8`,w)!;PA  ,́w)!;PAhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TTbyhLP2% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ 7 CBB,$G,,8`,w)!;h  ,́w)!;hhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w0. X@,UwX. ,$Gy=y=&ewpdv%    I}TT51LPs?%% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ DAB\B,$G,,8`,w)!;1  ,́w)!;1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wt. X@,UwX. ,$Gy=y=&ewpdv%    I}TT6M <ALP2% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ 8 DBB,$G,,8`,w)!;<A(  ,́w)!;<Ahw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TTNeTLP2% ( " " FEMF+*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ 8 C>CB,$G,,8`,w)!;T0  ,́w)!;Thw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. @,Uw. ,$Gy=y=&ewpdv%    I}Tl%A+1LX-----LD% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ CCB,$G,,8`,w)!;+1dR  ,́w)!;+1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}T`A1LT+ '% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱  C>CB,$G,,8`,w)!;1 0R ,́w)!;1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TlA 1LX-----?% ( " " FEMF+*@$??@DUD*@$??@DUD*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ CBB,$G,,8`,w)!; 1$R  ,́w)!; 1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,wL. @,Uw. ,$Gy=y=&ewpdv%    I}TTK4sQ1LPn?)% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ CAB\B,$G,,8`,w)!;Q1  ,́w)!;Q1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TTtZzALP1% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱  DBB,$G,,8`,w)!;zA | ,́w)!;zAhw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w. X@,UwX. ,$Gy=y=&ewpdv%    I}TT"4J(1LPn)% ( " " FdXEMF+*@$??@DUD*@$??@DUD@ !!K@0   # ??@DUD$$??@DUD  Rp"Arial,l,A0_঱ T DAB\B,$G,,8`,w)!;(1 l ,́w)!;(1hw p,Yt._y=/_y=`0_&ewp,aw,GDIC@,w`. 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$K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x   3 A"h b 12pbU͹Π=04 nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x   3 A"h b 12p bU͹Π=0K2 nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x   3 A"h b 12p bU͹Π=0bE nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x   3 A"h b 12?@ABCDEFGHIJKLMNOPQRSTYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~d wsp:val="009A5689"/>p bU͹Π=0yX nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x   3 A"h b 12p bU͹Π=0k nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12p bU͹Π=0~ nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0 nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0դ nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0 nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0 nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0 nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=01 nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0H nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0_ nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0v* nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0= nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b 12pbU͹Π=0P nU͹Π=0PNG  IHDR*sRGB pHYs+IDAT(S ]4ajBE{AQD`n".iQ ? $K:^H Ș/HZآ.r֬`Dvo9&Mܹo0O{fdVIENDB`Dd x  3 A"h b?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~l 1#% EMFr\KhCF, EMF+@XXFtEMF+@ @ 0@?!@ "@ *@$??@ ! " FEMF++@ @ !@ @ *@$??!@ +@ @ !@ 2@;E E@ *@$??!@ *@$99*@$99*@$99+@ *@$99*@$99 @$ K JJ!b $$>>'% % V0 LF]LF]% % $$AA" FEMF+*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??C D*@$??C D*@$??C D*@$??C>D*@$??C>D*@$??C>D*@$??C D*@$??C\D*@$??C D*@$??CzD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD*@$??CD*@$??C D*@$99*@$??C D*@$??C D*@$??C D*@$??C>D*@$??C>D@ !!K@0   # ??C>D$$??C>D  RpTimes New Romanp@DC@,,,._, t ,._,,,` P  2_1PaIGhw p,Yt._$</_$<`0_&ewp,aw,GDICX,wf @,Uwf @9wJw&ewpdv%    T,na%LLower Bound: LxC2I,*C2888!% ( " " FxEMF+*@$??C>D*@$??C D*@$??C\D*@$??C D*@$??CzD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD@ !!K@0   # ??CD$$??CD  RpTimes New Romanp@7DC@,,`,w!aP~ %c`,́w!ahw p,Yt._$</_$<`0_&ewp,aw,GDICX,w8f x@,Uwxf @#<$<&ewpdv%    TNa LdUpper Bound:H88,*C2888!% ( " " FEMF+*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD@ !!K@0   # ??CD$$??CD  RpTimes New RomanHpCC@,,`,w!aӸ ,́w!ahw p,Yt._$</_$<`0_&ewp,aw,GDICX,wܦf @,Uwf @#<$<&ewpdv%    TTHsZLPp_.% ( " " FdXEMF+*@$??CD*@$??CD@ !!K@0   # ??CD$$??CD  RpTimes New RomanPA BBB@,,`,w!Z=,́w!Zhw p,Yt._$</_$<`0_&ewp,aw,GDICX,wf X@,UwXf @#<$<&ewpdv%    TTICd.nLP1s% ( " " FdXEMF+*@$??CD*@$??CD@ !!K@0   # ??CD$$??CD  RpTimes New Roman0BpCC@,,`,w!.n==,́w!.nhw p,Yt._$</_$<`0_&ewp,aw,GDICX,w̮f X@,UwXf @#<$<&ewpdv%    TlyAs^ZLXand p*...% ( " " FdXEMF+*@$??CD*@$??CD@ !!K@0   # ??CD$$??CD  RpTimes New RomanC BBB@,,`,w!^ZN ,́w!^Zhw p,Yt._$</_$<`0_&ewp,aw,GDICX,w(f X@,UwXf @#<$<&ewpdv%    TTBC]'nLP2s% ( " " FdXEMF+*@$??CD*@$??CD@ !!K@0   # ??CD$$??CD  RpTimes New RomanCpDC@,,`,w!'n==,́w!'nhw p,Yt._$</_$<`0_&ewp,aw,GDICX,wlf X@,UwXf @#<$<&ewpdv%    T\ssXZ-Lare the sample proportions of the two samples*#%.% *C.%.#*.*%*. *.%=* *C.% % ( " " FEMF+*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD@ !!K@0   # ??CD$$??CD  RpTimes New RomanH0EB@,,`,w!XZ@ -,́w!XZhw p,Yt._$</_$<`0_&ewp,aw,GDICX,wf @,Uwf @#<$<&ewpdv%    T EP?LNote: the same requirements hold as for the hypothesis testing_<*%.% *C%#%..#%C%. .*.* *#.%.*.*.%  % .*% ( " " F EMF+*@$??CD*@$??C D*@$99*@$??C D*@$??C D*@$??C D*@$??C>D*@$??C>D*@$??C>D*@$??C D*@$??C\D*@$??C D*@$??CzD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??CD*@$??C D*@$??CD*@$??C D*@$??CD*@$??CD*@$??CD*@$??C D*@$99*@$99+@ *@$99*@$99*@$99+@ *@$99*@$99*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$??foDX:D*@$99*@$??foDX:D*@$??foDX:D*@$??foDX:D@ !!K@0   # ??foDX:D$$??foDX:D  RpTimes New RomanpQCC@,,`,w!P3? 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