Week14-2up - 318 Confidence Interval: Test Statistic:...

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Unformatted text preview: 318 Confidence Interval: Test Statistic: estimator (table value)(standard error) £   ¡   DIFFERENCES Method of Analysis : do a one-sample “t” ON THE Assumptions: Differences appr. Normally dist. Last Time : Paired-Difference Experiments Chpts 7, 8, 9 Wednesday : Systematic approach to material in problems on syllabus! 9.60, 9.97, 9.100, 9.107 and rest of Chpt 9 For Tuesday : Exer. 9.46, 9.52–54, 9.56, 9.59, Today : p. 402 – 406 Wins Lottery”? Thought: Why don’t you ever see the headline ”Psychic STA 2023 c D.Wackerly - Lecture 23 ¡  ¢ £ ¨©  ¤ ¦ §¥ © ¨© © Basic Statistics Paired SE Mean 8.98 6.79 3.43 95% CI for mean difference : (1.39, 19.01) T-Test of mean difference = 0 (vs > 0): T-Value = 2.98 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 Click OK, OK. value 319 P-Value=0.015 Choose alternative (Greater than in this case), null Click Options, type in confidence level (for CI) Variable 2. (After in this case) Click in box labelled ”Second”, double click on Variable 1 (Before in this case). Click in box labelled ”First”, double click on Stat Punch in data values Minitab? STA 2023 c D.Wackerly - Lecture 23          ¡ male managers, ¢ ¡ of females managers married. of the male female managers 320 ¢ ¢  ©   ©      ¢ (Male = “1”, Female = “2”). female managers who are married. Find a 95% CI for difference in proportions of male and managers married, § from Fortune 500 corporations. women. £ Ex. # 9.54, p. 407 Managerial careers of men and ¨ ¢ £¤ ¥¦    ¢ attribute attribute from pop 2, from pop 1, Independent samples: Pop 2 Pop 1 Have: Two populations Independent Samples (p.402) Comparing Two Population Proportions STA 2023 c D.Wackerly - Lecture 23     § ¢ # # with attribute estimates estimates estimates # with attribute (p. 402) (p. 402) is approx. normally dist’d when both are large. (p. 402)  ©   ! ©  ! ©  © ¤    ©  ©  " © " © ¢ ¢  ©  ¢ ¢ ¢         ¤  ©     %  ¤ ¢ ¢ $      ¢ $      ¢   ¤  STA 2023 c D.Wackerly - Lecture 23 ’s 321  estimator formula sheet   (P. 403) ¢ table CI for standard errors formula sheet male managers, £ ¢ ¡ of the male female managers 322 of females managers married. ¥¦  (Male = “1”, Female = “2”).  ©   ©  ¢ ¢ ¢  ¢       ¥¦ ¨ ¢  female managers who are married. Find a 95% CI for difference in proportions of male and managers married, § from Fortune 500 corporations. women. ¨ ¢ § £¤ Ex. # 9.54, p. 407 Managerial careers of men and  ©  ¡¦ Large Sample   ¤ STA 2023 c D.Wackerly - Lecture 23 © ¨  ¡   £  ¢        ©  ¨    ¤  ©    ¥ $ ©      ¦  % ¡ ¢ £ Confidence interval: STA 2023 c D.Wackerly - Lecture 23 confidence level , the proportion of male and female managers who are married by between managers who are married exceeds the proportion of At the £ §  © ¢ ¡ ¢ ¢  ¢   § ¢  ©   ¤ ¡  ¢  § $© ¢    ©   £  ¢    ¢  £¤ #$  ¢  © % ! " $ ©  ¢  ©  ¢   $ ©     ¢ % 323 versus OR OR RR or larger score (tail area) smaller score p-value a fixed particular value of difference Consider testing (p. 404) 324 hypothesized value on formula sheet. standard error total sample size total # “S” in experiment with , estimate this , use the individual ’s , then 325 NULL HYPOTHESIS standard error COMMON value of If If Formula Sheet estimator TEST STATISTIC STA 2023 c D.Wackerly - Lecture 23    STA 2023 c D.Wackerly - Lecture 23 ¦ ¡      ¤ ¥ ¢¦ ¤   ¤ #   ¤ ¤ ¢£ ¡  ¢ ¥ ¥ ¥  ¥ # # #   ¥  ¤ ¤ ¤ ¥  ¤        ¤     ¨§£  ¤      ¢ # ¥ ¢   ¢ ¥ ¢¦ # © ¤   ¢ ¢    % % §   ¢    $ ¢ $   §     ¤   ¢  ©©    %   © § % ¢    ¥ # $     ¤   ©©    ©© 326 Use of true prop. of premi’s given inositol with eye on standard diet had eye injuries. compensate for poorly developed lungs Is ? tail test, eye injuries RR : true prop. of premi’s not given inositol with injuries (2) (1) premature infants given inositol had an eye injury to to high oxygen levels used to of . reduce the risk of eye damage in premature infants? Test Statistic STA 2023 c D.Wackerly - Lecture 23  level, there P-value : Lower tail test – oxygen levels for infants given inositol. of premature infants with eye injury due to high p-value 327 evidence to claim a lower proportion Decision : at the  Ex. : # 9.107, p. 431 Does inositol (found in breast milk)         £¡   ¨ ¥   ¢   ¢  ¦     ¢  ¢£ ¡ ¡ ¢ # ¢    ¢ ¢ ¤   ¢ ¤   ¢  $ STA 2023 c D.Wackerly - Lecture 23   ¢ %  % ¢ ¡  ¢    ¢ ¢ ¢ ¢   ¨  ¢ ¢¤   §  ¢ ¤   ¢ #  %   ¥ ¤    -value larger than – Claim  – Claim  – ? ? ? significantly lower for any    ¥ , claim a lower proportion with breathing irregs if given inositol. Not  ¢     For any ¢   ¢  ¢  ¢   328 Stat Basic Statistics 329 Click in box ”Use pooled estimate for p for test”. Choose alternative (Less than in Ex 9.107) Click ”Options” type in # successes (29 in Ex 9.107). trials (110 in Ex 9.107), in box labelled ”Successes” ”Second Sample” in box labelled ”Trial”, type in # of type in # successes (14 in Ex 9.107). trials (110 in Ex 9.107), in box labelled ”Successes” ”First Sample” in box labelled ”Trial”, type in # of Click Radio button “Summarized data” 2-Proportions Minitab? STA 2023 c D.Wackerly - Lecture 23 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 Sample 1 2 Test and Confidence Interval for Two Proportions Click OK, OK   ¢   STA 2023 c D.Wackerly - Lecture 23 ¢        samples from? or or (c) Hypothesis Test (reach a decision) (b) Confidence Interval (a) Find Sample Size(s) 3. What is the OBJECTIVE of the exercise? (b) 2 Populations : (a) 1 Population : 2. What is the PARAMETER if interest? (c) More than 2 (STA3024) (b) (a) . with confidence units standard error table formula sheet estimator form. sheet table value (b) Confidence Interval with confidence coefficient     Estimate to within ¤ 1. How many POPULATIONS have I taken (will I take)  £   (a) Sample Size    §    ¤ §      Systematic Approach to Chapters 7, 8, 9  4. How to proceed?  acquired by age 18. -Albert Einstein small S.S. large S.S.  Thought: Common sense is the collection of prejudices  ¤  STA 2023 c D.Wackerly - Lecture 24  330 § STA 2023 c D.Wackerly - Lecture 24 331 std. error form. sheet  §  ¡       ¡ §   ¡ ¡ ¤     ¢      Parameter OR “something” OR “something” “something” “something” – How about sample(s) Test Statistic Param Param Param What am I “trying to prove”? : i. Large ( ) or small ( )? ii. Independent or Paired? 332 Large Sample(s) STA 2023 c D.Wackerly - Lecture 24 estimator hypothesized value standard error Param Param Param “something” OR “something” OR “something” Hypothesized Value from NULL HYPOTH. or Estimator and Stand. Error from Form. Sheet ¢ (c) Hypothesis Testing ¢ ¡ ¤    ¦ ¡ ¤ STA 2023 c D.Wackerly - Lecture 24  £¥£¡£¡£¡¤¡£¡£¡£¡¢ ¡ ¢ ¨¨ ¨ ¢ £ ¥ § ¤  £¥£¡¤¡£¡£¡£¡£¡£¡£¡¤¡£¡¢ ¡ £¦£¡£¡£¡£¡£¡£¡£¡£¡£¡£¡¡ £¦£¡£¡£¡£¡£¡£¡£¡¡    ¥ ¢¦  ¥ ¥   ¤ ¤ ¢¦ § ¤    ¤    ¡ §§ 333 RR ££¡¤¡£¡£¡£¡£¡£¡£¡¤¡£¡¡ © ££¡£¡£¡£¡£¡£¡£¡£¡£¡£¡¡ ¢ £  Param Param Param , not ¡ ¡ OR “something” OR “something” the calculated value of “something” . 2. Independent Samples (assuming 1. ¡ Small Sample(s)  ¨ # d.f. calc ) (tail area) calc Calculate DIFFERENCES for all pair 3. Paired Samples   £¥£¡¤¡£¡£¡£¡£¡£¡¢ ¡ £¦£¡£¡£¡¤¡£¡£¡£¡¡ ¢ ¤ ¥ ¢¦      P-values : calc differences. Use one-samp. proc. to analyse the ¡    ¢   ¤  ¨     %  §£  %     ¤  ¥ ¤ p-value known. 2. Use if “large” unknown 1. Use if “small” 5. Use for CI or tests : Large Samples 4. Use for test 3. Use for CI . Formula Sheet STA 2023 c D.Wackerly - Lecture 24      ¤   ¦ 8. Use to test 7. Use for CI or test 6. Use for CI or tests : Small Samples ¦  ¡ ¡ ¡ ££¡¤¡£¡£¡£¡£¡£¡¡ © # #  ¡ ¡   ££¡£¡£¡¤¡£¡£¡£¡¡  ¨  ¢ ¦  ¤ £   334 ¢  STA 2023 c D.Wackerly - Lecture 24  335 Use “system” for several examples from text. STA 2023 c D.Wackerly - Lecture 24 336 ...
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This note was uploaded on 07/28/2011 for the course STA 2023 taught by Professor Ripol during the Fall '08 term at University of Florida.

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