Week14-4up - 318 STA 2023 c D.Wackerly - Lecture 23 STA...

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Unformatted text preview: 318 STA 2023 c D.Wackerly - Lecture 23 STA 2023 c D.Wackerly - Lecture 23 319 Thought: Why don’t you ever see the headline ”Psychic Minitab? Wins Lottery”? ' Punch in data values Today : p. 402 – 406 ' Stat For Tuesday : Exer. 9.46, 9.52–54, 9.56, 9.59, ' Click in box labelled ”First”, double click on Paired ¡ ( ( 9.60, 9.97, 9.100, 9.107 and rest of Chpt 9 Basic Statistics Variable 1 (Before in this case). problems on syllabus! ' Click in box labelled ”Second”, double click on Last Time : Paired-Difference Experiments ' Click Options, type in confidence level (for CI) Assumptions: Differences appr. Normally dist. ' Choose alternative (Greater than in this case), null Wednesday : Systematic approach to material in Variable 2. (After in this case) Chpts 7, 8, 9 Method of Analysis : do a one-sample “t” ON THE DIFFERENCES value ' Test Statistic: Paired T for Before - After N Mean StDev Before 6 166.27 22.00 After 6 156.07 16.64 Difference 6 10.20 8.39      ©§¥ ¨¦¤ £¡ ¢ 95% CI for mean difference : (1.39, 19.01) T-Test of mean difference = 0 (vs > 0): T-Value = 2.98 (table value)(standard error) P-Value=0.015   %#!  &$"¡ estimator SE Mean 8.98 6.79 3.43 ¤ STA 2023 c D.Wackerly - Lecture 23 320 Confidence Interval: Click OK, OK. STA 2023 c D.Wackerly - Lecture 23 321 Comparing Two Population Proportions Independent Samples (p.402) Have: Two populations female managers who are married. (Male = “1”, Female = “2”). from pop 2, # with attribute # with attribute estimates estimates estimates (p. 402) (p. 402) is approx. normally dist’d when both are large. (p. 402)  Find a 95% CI for difference in proportions of male and from pop 1, ¥D % B C EB C ' %  hiDH e¢ aUYX1UB c' d `B WV b D % f % C 1fgD C ¥D `B WV S % C EC ¢ aUYX1UB T' ¥ ¥ %C DC % BC D BC  % G¢ C F %B %C % D F D G¢ D B C of females managers married. Independent samples: DC @2 3A managers married, of the male attribute F 20 31) from Fortune 500 corporations. Pop 2 % D female managers attribute ¢% ¢DF @958 64 754 male managers, PQI P QI women. Pop 1 %C ¢R DC ¢R Ex. # 9.54, p. 407 Managerial careers of men and ’s D ¢ H ¢%  ¢ % G¢ F % D ¢ D G¢ F D EB C % BC ¡ © § ¥ £ ¡ ¨¦¤¢ 323 CI for (P. 403) %# ¢ &$! 6 5' 4 2 54 ' ¢ 2 30 % h D D % Bf % B C 1Bf D B C 2 4 2 30 0 R& $ )# formula sheet ¢ 8% 7 &$ P " &# )!# % standard errors table Confidence interval: ¢1 @2 30  £  % &# ! hD %  iH D % Bf % B C 1Bf D B C " ' ( & $ %# " formula sheet ! estimator STA 2023 c D.Wackerly - Lecture 23 322 1 Large Sample STA 2023 c D.Wackerly - Lecture 23 R % C ¥ D CP B B ' ¦ female managers who are married. At the confidence level , the proportion of male (Male = “1”, Female = “2”). managers who are married exceeds the proportion of ¢ female managers of the male ¢ 2 30 of females managers married. @2 330 female managers who are married by between STA 2023 c D.Wackerly - Lecture 23 estimator ¢ T F¢ 2 2 , then , estimate this with total # “S” in experiment total sample size h  % F h D i¢ R C DF R f H RC W R R % ¢ on formula sheet.  h H D ¢ RC standard error U e% § ¥ ¥ ' ' (tail area) c dT § 6 6 W COMMON value of c ¢ If , use the individual ’s I PI 6 ' ¢ Q 5Q H G4 ! P I ! P I or score If C C ¢%C ¢DC R `aYP R C b X D h H VAU % d D % f H % C 1f H D C § ¥ S¥ ER C R %C D 6 ¥ A© @ ¢%C DC § C ' ' @ ¥ § ' E % &#$! ' C % &# ! ' ¥ 6 6 ' E ' 6 C D% E D% § ' B 9 OR smaller score NULL HYPOTHESIS I PI Q OR larger Q 5Q ' 9 versus p-value standard error Formula Sheet a fixed particular value of difference RR hypothesized value I ' Consider testing (p. 404) 325 TEST STATISTIC ¢ 324 I 958 0 STA 2023 c D.Wackerly - Lecture 23 ¥ @2 3A  2A 0 ¢ % F ¢ % BC % D D ¢ D F ¢ EB C 64 754 ¢ %  2301) ¢ H D and I PI 20 31) Find a 95% CI for difference in proportions of male and ¢ 2) @958 64 754 from Fortune 500 corporations. managers married, d male managers, h R % C ¥ EC P B DB ' ¦ women. % &# ! Ex. # 9.54, p. 407 Managerial careers of men and C ¥ EC D C ¥DC § ¢ C ¥ EC D F G% STA 2023 c D.Wackerly - Lecture 23 Ex. : # 9.107, p. 431 Does inositol (found in breast milk) ' Test Statistic ' Decision : at the ¢ ' c c5c 2 30 premature infants given inositol had an 2 ¢ 1 of . R HR Ue%  h D  fC c cT § ¥ R C ¥ ER C D % reduce the risk of eye damage in premature infants? A Use 327 6 326 STA 2023 c D.Wackerly - Lecture 23 c ' eye injury to to high oxygen levels used to compensate for poorly developed lungs on standard diet had eye injuries. ¢ ' c 5c 2 C ¢ D ' 0 74 ' of true prop. of premi’s given inositol with eye injuries 1 ¥ D A© @ % C EC ¥@ %C DC B level, there evidence to claim a lower proportion of premature infants with eye injury due to high (2) oxygen levels for infants given inositol. RR : ' P-value : Lower tail test – p-value ¢ ( 2 0 c ¢ % RC ¢ ¢ 1 ' ¢ 2 § 6 ' STA 2023 c D.Wackerly - Lecture 23 328 9 ¢ ¢ D RC h  D R F ¢ % F h D i¢ C % ¢ 0 9 ? ¢ C ¢ % ' Is 2 30 tail test, (1) A6 772 ¢ eye injuries ¢ true prop. of premi’s not given inositol with STA 2023 c D.Wackerly - Lecture 23 329 Minitab? ' ' ' ”First Sample” in box labelled ”Trial”, type in # of c , claim a lower 2 22 530 1 ' proportion with breathing irregs if given inositol. Not type in # successes (14 in Ex 9.107). ' ”Second Sample” in box labelled ”Trial”, type in # of 2 22 530 E 1 ? trials (110 in Ex 9.107), in box labelled ”Successes” 2 ¢ 1 a' 2 30 – Claim type in # successes (29 in Ex 9.107). c ? ' Click ”Options” ' Choose alternative (Less than in Ex 9.107) ' Click in box ”Use pooled estimate for p for test”. ' Click OK, OK ¢ 1 a' 2 30 – Claim 2 22 530 ¢ 1 a' – 2-Proportions trials (110 in Ex 9.107), in box labelled ”Successes” c significantly lower for any ( -value larger than Click Radio button “Summarized data” Basic Statistics ( For any Stat ? Test and Confidence Interval for Two Proportions Sample 1 2 X 14 29 N 110 110 Sample p 0.127273 0.263636 Estimate for p(1) - p(2) : -0.136364 95% CI for p(1) - p(2): (-0.239604, -0.0331235) Test for p(1) - p(2) = 0 (vs < 0) : Z = -2.55 P=0.005 330 STA 2023 c D.Wackerly - Lecture 24 STA 2023 c D.Wackerly - Lecture 24 331 Thought: Common sense is the collection of prejudices acquired by age 18. -Albert Einstein 4. How to proceed? (a) Sample Size confidence & ¢R standard error $ )# ' c 4 table formula sheet b c &$ P " %&# )!# ' " R1 ¥ P H (b) c (a) 2 52 with units @ ' samples from? Estimate to within b 1. How many POPULATIONS have I taken (will I take) ¡ Systematic Approach to Chapters 7, 8, 9 (c) More than 2 (STA3024) (b) Confidence Interval with confidence coefficient H & $ %# @ @ " & $ %# " %#! &$X¡ %# &$! ' ¥D % C EC C S ¥D % S HS 3. What is the OBJECTIVE of the exercise? P" form. sheet table value std. error $ %# ¥P estimator 0 R& c 1 . R or H (b) 2 Populations : c or 2 52 (a) 1 Population : @ 2. What is the PARAMETER if interest? form. sheet large S.S. small S.S. (a) Find Sample Size(s) (b) Confidence Interval (c) Hypothesis Test (reach a decision) 332 STA 2023 c D.Wackerly - Lecture 24 STA 2023 c D.Wackerly - Lecture 24 333 Large Sample(s) (c) Hypothesis Testing standard error ¦ ¢ ' C ¨ Hypothesized Value from NULL HYPOTH. ££ ' ' £ ££ ££ ££ ££ ££ £ or ££  ' ¥ %&# ! ' C ¥ % &# ! ' ' ' E ' “something” RR ££ E ¤ ££ ££ F¢ ££ Param E ££ OR ! “something” ££ E ££ ¤ @ ££ ££ F¢ B 9 B 9 ££¥ ¢ @ © £¥ ££ ££ ¡ ' ii. Independent or Paired? £ ££ ££ Param 9 – How about sample(s) i. Large ( ) or small ( )? C OR “something” Test Statistic “something” C ¢££ Param “something” ! ££ OR ££ ¨ ©¨ ££ ££ “something” Estimator and Stand. Error from Form. Sheet ££  ' ¢££ Parameter hypothesized value “something” OR Param ¦ Param ¥ Param estimator ¦ §¦ What am I “trying to prove”? : ' ' Formula Sheet £ unknown ¡ “small” ¡ ¡ 'P YI £ '  ' H G4 £ ££ ££ E ¤ ££ ££ B 9 £ ££ F¢ £¥ Small Sample(s) “large” ' £ ££ ' (tail area) known. b R ££ E ¢££ £ “something” 1. Use if 2. Use if p-value ££ calc ££ C Param 'P YI OR C “something” ' Param calc R OR £ ££ ' “something” ' Param 335 ££  ¢ the calculated value of STA 2023 c D.Wackerly - Lecture 24 b P-values : calc 334 STA 2023 c D.Wackerly - Lecture 24 3. Use for CI . 4. Use for test 9 5. Use for CI or tests : Large Samples %% 6. Use for CI or tests : Small Samples ¡ ¡ & R34 ¥ )$ # h D  P " ¥  P % h D  R ¥ D  P ¢ %U  % %c ' ¡ ' Use one-samp. proc. to analyse the differences. STA 2023 c D.Wackerly - Lecture 24 Use “system” for several examples from text. 336 9 c Calculate DIFFERENCES for all pair ¥ D D© @ ¢ % C EC R X` 8. Use to test 3. Paired Samples 2 7. Use for CI or test # d.f. P ) X` ' 2. Independent Samples (assuming . R ¡ , not © C C@ © ¢ 1. ...
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