MAT 122 Week 8 Notes
MAT 122 Week 8 Notes MAT 122 - M100
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This 5 page Class Notes was uploaded by Samantha Harrington on Friday October 23, 2015. The Class Notes belongs to MAT 122 - M100 at Syracuse University taught by A. Bourhim in Fall 2015. Since its upload, it has received 67 views. For similar materials see Probability and Statistics for the Liberal Arts II in Mathematics (M) at Syracuse University.
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Date Created: 10/23/15
MAT122 Week 8 Notes Sign Test 0 Nonparametric test or distributionfree test Claims involving matched pairs of data Claims stating that there is no difference between two data Claims about the median of a population 0 Uses and signs to analyze their frequencies and determine whether they re significantly different Process is on Pg Claims Involving Matched 0 For each pair we subtract the value of the second variable from the value of the first one Assign If the difference is positive If the difference is negative 0 If the difference is 0 Notation 0 X the number of times the less frequent sign occurs 11 the total number of and combined ignore the 0 s 0 Ho 2 the median of the difference 0 there is no difference 0 H1 2 the median of the difference i 0 Or the median of the difference gt 0 Or the median of the difference lt 0 Requirements The sample data are randomly selected No other requirement Caution When applying the sign test in a onetailed test we need to be very careful to avoid making the wrong conclusion when one sign occurs significantly more often than the other but the sample data contradict the alternative hypothesis If the sample data contradicts the alternative hypothesis we fail to reject the null hypothesis Test Stat lfn S 25 the test stat is X Use Table A7 Pg 733 lfngt25use n ch06 1 H m 7 Example Listed below are ages of actresses and actors at the times that they won Oscars The data are paired according to the years that they won Use the sign test and a 005 significance level to test the claim that there is no difference between the ages of the best actresses and the ages of the best actors at the time the awards are presented Actress 2 32 2 24 210 21 25 lg 1 10 2 Afton 01 ll 52 m sq LlD 6b Ln 5 20 1 WWquot quot39 quot quot x L W OQ0D 5 3 H H mum MD QWEWCRCC OPPBSHC Dl rtnCC HD 2 0 medicm I we dwarfnot H1 2 mcdiwn of m diff crmcc at D 44 1 U H hlv 250 the st stout is X Ll took 1 Tobie A at maximum A3 xsvk e UOt tom to rcjcct RD mm mm Thoratom wt mu TD raw thc chum mot Example Listed below are the scores of Test 1 and Test 2 of math class Use a 005 significance level Tesmzqo C15 8 6 80 st Loo aw 3 101 Testzti qsb Eslo lt15 an Lalo a2 a 2 Sign t 3 i3 szd005 to n q H01 N0 dlfPCrthCC th x cm 0 ditttrmct D H39 th iom 0 dif rcncc 0 tun v mum U Example without a long explanation To test the claim that there is no difference between the lifetimes of two brands of batteries we found 15 16 g Y 3 0 n 31 17 7 25 Use a 005 significance level to test the claim that there is no difference in the lifetimes web 2 d 005 alum ND Olme lCC m2 Tm maxim O DPPDltt Tht mtdiom at o H Tht median 0 H0 Tht median 0 mm mud Tts r n m 8qu As r1 3 7 25 the new on is g z 03957 2 FL 31 50s Z Z 2 D a z Cusxbn 0300qu H condusum mt am TD 0 r95 reject H0 Thus wt 6 VB mu To rqtd the B I drum itsclt I I mm Runs Test for Randomness Used to determine whether sample data in a sequence are in random order Requires that data can be categorized into two separate types or categories Run 2 a sequence of data having the same characteristic uses the number of runs to test for randomness in order of the data Not based on frequency Notation 0 H0 the data are in a random sequence 0 H1 the data are in a sequence that is not random 0 m the number of sample data of the first type category 0 m the number of sample data of the second type category 0 G the number of runs Test Stat lfnl S 20 and m S 20 and o 005 the test stat is G Use Table A10 Pg 736 Reject randomness if G is Less than or equal to the smaller critical value from Table A10 0R Greater than or equal to the larger critical value from Table A10 Example Listed below are the genders 0f 18 individuals participating in a game Use a 005 significance level to test for randomness in the sequence of genders FMMFFFMMFMMMMFFFFF it u 2 3 a 5 a a Z 2 is meats 86mm n cioezb a n1 22001005 m tts r we is 61 C cm Ullle 5 and 16 tbmmsmn mt mu TD quot uI 1 WWW rqcc r H0 Wham 5 a 15 1 tom ti 4 H 47 mm 8 rm mndO mm it 0 danced rcqnm Test Stat a 396 If m gt 20 and m gt 20 and 0 005 the test stat is i 39 W Where MG 3 Zn 7 Jr n3 n2 And Ga 5 31 n2 In ll 307 03001013014 Reject randomness if the test statistic 2 falls in the critical region Use Table A2 for critical values Example Listed below are the genders or 3951 individuals participating in a game Use a 001 significance level to test for randomness in the sequence of genders MFFPPMMMMMMFFFFFFFMMMFFFMMMMFFFFFFFF mfgel llm 3 H0 mmumntss n 71 MKS a na Btcuusc n 2 2 gt20 tht ts we is 1 96 a 2mm H 3 21227079 H nlfn l 139 T znln232nnz n n5 n39n2z n 23917 ZXZZXWOCZ X Z le Z Ll75 Z ZMQN LNQ I 73 341 a z quot w idiom mime k2 9e 9 3mm 7 4145 tons in at mmm Vtgwh wt rqwc RD ind marctbrc mt rqcc v mt randomness
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