# Week14 - STA 2023 c D.Wackerly - Lecture 23 318 Thought:...

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Unformatted text preview: STA 2023 c D.Wackerly - Lecture 23 318 Thought: Why don’t you ever see the headline ”Psychic Wins Lottery”? Today : p. 402 – 406 For Tuesday : Exer. 9.46, 9.52–54, 9.56, 9.59, 9.60, 9.97, 9.100, 9.107 and rest of Chpt 9 problems on syllabus! Wednesday : Systematic approach to material in Chpts 7, 8, 9 Last Time : Paired-Difference Experiments Assumptions: Differences appr. Normally dist. Method of Analysis : do a one-sample “t” ON THE DIFFERENCES Test Statistic: ¨ ¦¥  ©§ ¨ ¤£ ¢¡ Conﬁdence Interval: (table value)(standard error) ¨ ¨§   ¡ £  estimator STA 2023 c D.Wackerly - Lecture 23 319 Minitab? Punch in data values ¡ Basic Statistics Paired ¡ ¡ Stat Click in box labelled ”First”, double click on Variable 1 (Before in this case). Click in box labelled ”Second”, double click on Variable 2. (After in this case) Click Options, type in conﬁdence level (for CI) Choose alternative (Greater than in this case), null value Click OK, OK. 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 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 P-Value=0.015 STA 2023 c D.Wackerly - Lecture 23 320 Ex. # 9.54, p. 407 Managerial careers of men and male managers, ¦© §¥ ¨¦¥ £¡ ¤¢ women. female managers from Fortune 500 corporations.  £  managers married, of the male of females managers married. Find a 95% CI for difference in proportions of male and female managers who are married. (Male = “1”, Female = “2”). ¢ ¢  ¢   ¢    ¢   ¢   STA 2023 c D.Wackerly - Lecture 23 321 Comparing Two Population Proportions Independent Samples (p.402) Have: Two populations ¢ ¢ ¡ attribute ¢ ¡ Pop 2 ¢ attribute   Pop 1 Independent samples: # with attribute ¤ (p. 402) (p. 402)  ¤   ¢    ¤ ¢            is approx. normally dist’d when both © §¥ ¢ ¤ ¨¦¤ £ ¢ © ¤ § ¥ ¤    ¤   are large. (p. 402)           estimates   estimates  ¢ estimates   from pop 2, # with attribute  ¢ from pop 1, ’s STA 2023 c D.Wackerly - Lecture 23 322 £ ¢ ¡ CI for (P. 403) standard errors            ¡      formula sheet table  ¢ £               formula sheet ¦¥¤ estimator §§ ©¨¡ Large Sample ¤ ¢   ¡    Ex. # 9.54, p. 407 Managerial careers of men and male managers, ¦© §¥ ¨¦¥ £¡ ¤¢ women. female managers from Fortune 500 corporations. of females managers married.  £  managers married, of the male Find a 95% CI for difference in proportions of male and female managers who are married. (Male = “1”, Female = “2”). £¡ §¥¥ ¢ ¢ £ ¦©    ¢   ¢    ¢   ¢   STA 2023 c D.Wackerly - Lecture 23 323 Conﬁdence interval: ¢  § ¨  ¥£ ¦¤  ¢          £ ¢ ¥ ¡ ¢ £        ¥     £¡ ¡ ¢ ¢ ¤ ¢   ¡    ¢   ¢ ¡  ¡ © ¢   £¡ At the conﬁdence level , the proportion of male managers who are married exceeds the proportion of female managers who are married by between and STA 2023 c D.Wackerly - Lecture 23 324 Consider testing (p. 404) a ﬁxed particular value of difference ¥ ¥ ¢ ¤  ¡ ¦ versus ¢ p-value ¤ ¡ larger score ¢ RR  ¡ £  £   ¥ ¥  ¤ ¤ smaller score ¡  ¤ ¤ ¤  ¥ ¥   ¤ OR ¦ ¥ or (tail area) ¢ OR       ¤ ¤  £  ¥  ¥ ¥ ¢ ¤  STA 2023 c D.Wackerly - Lecture 23 325 TEST STATISTIC hypothesized value ¢ £¢ NULL HYPOTHESIS ¤  ¦   ¡ ¢  ¢  total # “S” in experiment total sample size ¥ ¢       ¤ ¦     ¤ ¥ ¢ ¤ ¢ ¤ ¢ on formula sheet. ¡ ¥ standard error  ¥ ¢ ¥ with   ¡ , estimate this ¡ ¢ COMMON value of ¦ §¡   ¤ , then © ¨ ¦  ¤  ¤ , use the individual ’s ¢ ¥ ¥  ¤  If  ¢ If ¥ ¤ Formula Sheet standard error ¡ estimator ¢ ¢ £¢ ¢ STA 2023 c D.Wackerly - Lecture 23 326 Ex. : # 9.107, p. 431 Does inositol (found in breast milk) reduce the risk of eye damage in premature infants?  ¢  ¡ ¢ premature infants given inositol had an ¡ of .  £  Use  eye injury to to high oxygen levels used to compensate for poorly developed lungs  £ on standard diet had eye injuries. ¡ ¡ of ¥ ¢ true prop. of premi’s given inositol with eye injuries ¢ true prop. of premi’s not given inositol with eye injuries  ¤  ¤  ¢ ¡ ¡ ¦ (2) ¢ ¡ RR : ? £¡  ¢ ¢ ¢ ¢  ¤   ¢   ¢ ¡     ¥ ¥ Is  tail test, (1) ¢ ¤ ¢  ¤ STA 2023 c D.Wackerly - Lecture 23 327 Test Statistic ¥   ¥ ¤  ¤   ¤  ¤ ¤ ¦ ¢ ¤  ¢ ¢ ¢  ¨§ £  ¢  ¡ © Decision : at the level, there evidence to claim a lower proportion of premature infants with eye injury due to high oxygen levels for infants given inositol. P-value : Lower tail test – ¢ p-value STA 2023 c D.Wackerly - Lecture 23  -value larger than £ ¡¡ ¤© For any 328 , claim a lower proportion with breathing irregs if given inositol. Not £ ¢  ¡ ¢  ¢  ¡ ¢ £ ¡  ¡ ¢ ¢ – ? – Claim  ? ¡ ¢ – Claim ¡ ¤ ? £ signiﬁcantly lower for any STA 2023 c D.Wackerly - Lecture 23 329 Minitab? Basic Statistics ¡ ¡ Stat 2-Proportions Click Radio button “Summarized data” ”First Sample” in box labelled ”Trial”, type in # of trials (110 in Ex 9.107), in box labelled ”Successes” type in # successes (14 in Ex 9.107). ”Second Sample” in box labelled ”Trial”, type in # of trials (110 in Ex 9.107), in box labelled ”Successes” type in # successes (29 in Ex 9.107). Click ”Options” Choose alternative (Less than in Ex 9.107) Click in box ”Use pooled estimate for p for test”. Click OK, OK 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 STA 2023 c D.Wackerly - Lecture 24 330 Thought: Common sense is the collection of prejudices acquired by age 18. -Albert Einstein Systematic Approach to Chapters 7, 8, 9 1. How many POPULATIONS have I taken (will I take) samples from?  (b) ¥ (a) (c) More than 2 (STA3024) 2. What is the PARAMETER if interest? ¤ or  or £ ¤ £ 3. What is the OBJECTIVE of the exercise? (a) Find Sample Size(s) (b) Conﬁdence Interval (c) Hypothesis Test (reach a decision)  £ (b) 2 Populations :  (a) 1 Population : . STA 2023 c D.Wackerly - Lecture 24 331 4. How to proceed? (a) Sample Size © units conﬁdence ¡ ¡ ¢ ¢ ¦   ¡ ¤  ¡        table formula sheet ¢   standard error © with ¡ Estimate to within (b) Conﬁdence Interval with conﬁdence coefﬁcient  ¦     small S.S. std. error   large S.S. ¡ ¡ ¡ ¢ ¦     ¡ ¤ ¡     form. sheet table value  ¢ ¡  estimator form. sheet    ¡ STA 2023 c D.Wackerly - Lecture 24 332 (c) Hypothesis Testing What am I “trying to prove”? : ¡ ¡ £ Param “something” ¡ ¡ ¡ ¡ ¡ ¡ OR ¢ ¤ Param “something” ¡ ¡ ¡ ¡ ¡ ¡ OR ¡ ¡ ¡ ¢ ¥ ¢ ¢ Parameter Param “something” “something” ¡ ¦ Test Statistic – How about sample(s) ¡ i. Large ( ) or small ( )?  ii. Independent or Paired? STA 2023 c D.Wackerly - Lecture 24 333 Large Sample(s) hypothesized value ¤ standard error ¡ estimator ¢  ¢ Estimator and Stand. Error from Form. Sheet ¢ £¢ Hypothesized Value from NULL HYPOTH. ¤ ¡  ¡ ¡ ¡ ¡ ¡ £ £  ¡ ¡ “something” ¡  Param ¡ ¡ ¡ ¡ ¡ ¡ ¡ OR ¡ ¡ ¡ RR ¡ ¡ ¡ ¡ ¤ ¤ ¤ “something”  ¡  Param ¢ ¡ ¡ OR ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ or ¡ ¡ ¡ ¥       ¤ ¤  ¥ “something” ¡ ¢ ¡ Param £ ¡ ¡ ¡ ¢   STA 2023 c D.Wackerly - Lecture 24 the calculated value of  ¤ ¢ P-values : calc 334  ¡ ¡ ¡ ¡ ¡ ¡ ¡   calc ¢ calc ¡ £  ¡ £ “something” ¡ Param ¡ ¡ ¡ ¡ ¡ ¡ ¡ OR ¡ ¢ ¡ ¡ ¡  ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¥ (tail area) ¦ ¥ ¢ ¢ ¡ . ¢ §  ¤ ¢ ¥  ¡   ¤    ¡    §¢  ¤  ¡  ¢ ¤§ # d.f. ) 3. Paired Samples Calculate DIFFERENCES for all pair differences. ¡ Use one-samp.   ¡ 2. Independent Samples (assuming ¦¨ ¡ , not proc. to analyse the ¥ ¡ ¡ “something” Small Sample(s) 1. ¡ ¢ ¤ OR Param p-value ¤ “something” ¡ Param STA 2023 c D.Wackerly - Lecture 24 335 Formula Sheet 1. Use if  known. 2. Use if  unknown “large” ¡  “small”   3. Use for CI ¦ ¢  4. Use for test . ¦ ¡ ¡ ¡ ¢ ¤  ¡ ¦ 8. Use to test 7. Use for CI or test ¦¨ 6. Use for CI or tests : Small Samples ¢ 5. Use for CI or tests : Large Samples STA 2023 c D.Wackerly - Lecture 24 Use “system” for several examples from text. 336 ...
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## This note was uploaded on 11/28/2011 for the course STA 2023 taught by Professor Ripol during the Fall '08 term at University of Florida.

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