Week15-2up_001 - Kelly Sodec Mathew Smeltzer Pavlina Rumcheva Terry Mashtare Saurabh Kumar Donte Ford David Finlay Adam Glassman David Ashley

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Unformatted text preview: Kelly Sodec Mathew Smeltzer Pavlina Rumcheva Terry Mashtare Saurabh Kumar Donte Ford David Finlay Adam Glassman David Ashley Shamshad Ali Sections ¡ ¡ ¡ ¡¦ Instructor ¡¢ ¨¡¦ ¡¦ ¡¦ ¡¢ ¡¢ ¡¢ ¦¦ ¡¢ ¡¢ ¤ ££ ¤  ¤ £ ¤ ¡ ¤ ¦ ¤ ¨£ ¥© ¤ ¨ ¤ §¨ ¥¡£ ¤ ¤ ¡¢ ¡¦ ¡¦ ¡¨¡ ¡¦ ¡¦¡ ¡¢ ¡¦ ¡¦ ¢¡¦ ¤¤ ¥©£ ¥¡£ ¤  ¤  ¤ £ ¥¡ ¤  ¤ § ¥©© ¤ £ ¤ ¤ ¡¦ ¡¢¡ 311 CAR 100 TUR L007 TUR L007 McC C 100 CSE A101 CSE A101 McC C 100 CAR 100 CAR 100 CAR 100 Location Final Exam Wednesday, May 1, 10:00 am – 12:00 noon Conflicts – see Wackerly NOW STA 2023 Final Exam Locations STA 2023 c D.Wackerly - Lecture 23 ¢£ ¡¦¡  ¡¡ ¡¦ 312 Last Time : Small sample inferences about problems on syllabus! 9.60, 9.97, 9.100, 9.107 and rest of Chpt 9 For Thursday : Exer. 9.46, 9.52–54, 9.56, 9.59, Wednesday : p. 402 – 406 9.94, 9.96, 9.101, 9.110, For Tuesday : Exer. 9.29, 9.33, 9.35, 9.38, 9.39, 9.42, Today : P. 389 – 396 Assignments STA 2023 c D.Wackerly - Lecture 23  £ ¡¡£ ¡¢ Assumptions: (p. 379) 1. : Same variances,  ¡¡ ©¦¡ ¦¡£ § ©§  ! 3. 2. : Independent samples. ! : Normal distributions. !     Pooled estimator for common variance STA 2023 c D.Wackerly - Lecture 23 C.I. for  Test Statistic estimator # d.f. (table value)(standard error) #   ¦  test stat estimator (standard error) hyp. value 313 314 Standard Deviation Mean Ingestion Time Number of urchins Construct a Decayed Blades 10 2.36 0.47 (1) 10 3.35 0.79 green and decaying grass. difference in mean ingestion times for urchins fed confidence interval for the (2) Green Blades to ingest the grass blades. The measurements were the time (in hours) necessary independently selected 10 were fed decaying grass. were randomly selected and fed fresh grass, another hours, then fed a 5 cm blade of turtle grass. 10 urchins Ex. : #9.26, p. 389 Sea urchins were starved for 48 STA 2023 c D.Wackerly - Lecture 23   ¡¢ £ ¥¤   §¤  ¦ !   ¨© ¦ ! ¦ ¤¤  !  ¤ ¦ ¤¦ ¦( "  " $# % & ¡ '   )  $ £ ¡ 3   " 6 5  4  " 75 ¦  1  8 20 £ 9  ¦ ¦ !  !  ¢ @ 90% CI : STA 2023 c D.Wackerly - Lecture 23 , ¡ £¦ d.f. or average time to consume decayed grass? sea urchins to consume green grass larger than the grass and decayed grass) Is the average time it takes (A bunch of “scholarly” words about sea urchins, green ©¢ # # © d.f. £ ¢£ $§ ¡  £¤ £  ¢ § ¨©  £ © £ "  " $# % & ¡ 3  ¦( ¤ ¤¦  315 STA 2023 c D.Wackerly - Lecture 23 , at the confidence level. All “plausible . necessary for the above test and CI to be valid? In terms of this example, what are the assumptions decayed) are values” for the difference in means (green vs. 9 –   ¤ ¦  ! ¤¦   ¦ ¤  ¡!  ¦  ! ¦  9  – – grass. decayed grass. 316 distributed a 5 cm blade of sea for both green and decayed grass. grass is approximately : the assigned to green and : the sea urchins in the study were ame for are approximately the : the POPULATION variances of     ) ¢ @ Sample sizes are small. STA 2023 c D.Wackerly - Lecture 23 ¡ ¨ Before ©  ¦ ¦ Subject learning biofeedback less than before? Use  ¦ ¦ After . not overweight? after learning biofeedback. Each individual subject had BP taken before AND 318 before and after the training. Mean blood pressure after 317 What happens if someone is careful about diet and ©¢ ¦¡¢ ¨¦ ¦   ¨ £ ¦ !  § ¦ £ ¦ ¦ ¦ ¦ ¢¨ §¢ ©¨ ¦ ¢ ¡ ¡ ¡ ¢ ¨ ¡!  £  ¡  ¦ £¢ Samples are will be low. HOW do we analyse the data??? – – – – What “factors” can impact BP? Why take before and after BP’s on same subject? independent!!! Is likely that both before and after BP measurement 9 9 9 9 9 9 © measurements (millimeters of mercury) were taken were taught biofeedback. Blood pressure biofeedback exercises on blood pressure. Six subjects Ex. : #9.101, P. 430 Study to assess the effect of STA 2023 c D.Wackerly - Lecture 23 9 9 for) (2) – (6). HOW?? Want: information about (1), compensating (controlling 6. Etc. 5. Driving habits of drivers 4. Road conditions and Surface 3. Speed driven 2. Weight of cars 1. Quality of the tires Things that influence mileage: cars – drive around – record mileages. Randomly select some tires of each brand – install on belted radial tires. Objective : Compare durability of two brands of steel STA 2023 c D.Wackerly - Lecture 23 319 How about left and right sides? installed on the front of each car. Randomly select one tire of each brand to be Method to consider : STA 2023 c D.Wackerly - Lecture 23 9 Can’t analyse data using method of Section 9.1 Problem : Samples are NOT independent This strategy will control for (2) – (6). 9 9 320 Treated wood last longer than untreated? PAIRED DIFFERENCE EXPERIMENT 9 Two brands of solar collectors : one better? 9 Before/After Experiments, Biofeedback #9.101 9 – By design to control for other factors manner. – Someone else collected the data in a paired Why Pair? 9 9 9 ¤9 Indep. ¥ 9  9  ¥ Popn. 1 . . . Pairs depen. depen. . . . differences depen. Popn. 2 Difference . . . same as if differences are taken “1”  NORMALLY distributed ASSUMPTION : the DIFFERENCES are approx.  £ ©© ©©   is NOT required . “2”. mean of the population of DIFFERENCES £ ¥  £  §  £ 1 §     ¨ 1 ¨ ¦  £ £ £  ¡¢ £ £ £ £ ¡¢ ¡¢ ¦ £ £ £ ¤  ¤  ¤ 5 ! 321 322 Subject less than before? Use Before After . Diff. training. Mean blood pressure after learing biofeedback (millimeters of mercury) were taken before and after the were taught biofeedback. Blood pressure measured biofeedback exercises on blood pressure. Six subjects Ex. : #9.101, P. 430 Study to assess the effect of DIFFERENCES Method of Analysis : do a one-sample “t” ON THE STA 2023 c D.Wackerly - Lecture 23 ¦ ¨  ©  £ 1 20  ¦ ¦ ¦ ¥ ©© ©¢  ¨ £ 1 20 ©© ¦¡¢ ¨¦ ¦  § ¡ £ ! ¦  ¦ ©¨ ¡ ¢  £ ¦ ¦ ¦ ¡ ¡ ¢ ¢¨ §¢   ¦ Totals ¨ ¡ ¦ ¢¦ ¦ ¦ £¢ ¡! ¦ ¡¢ ©  £   ¡  STA 2023 c D.Wackerly - Lecture 23 Diff.   ¡ ¢¦ ¦¦ ¡ £ §¡ © ¨¡ §£  ¡ ! ££ § £ §£ ¡£  £ £ £ ¢ ¥ " ¥  ¥ £ ( ¦ £ ¤£ ¦ £ ¤   ¥ £ ¤ ! ¤ ¥ ¡ ¢§ $ £ " ¥ ¨  ¥¤ level there learning biofeedback. that the mean blood pressure reading is higher before Conclusion : At the ¥ £¢ £ ¨ ¡ ¢§   ¥ ¥ 10 ¤  d.f. ¡  © £¢ © $ £¢ £ 1 © § 1 §  ¨  ¨ £ ¢£ £ ) ¥  £¢ Mean blood pressure larger before than after? ¦§  £ P-value? d.f. estimator C.I. for ¡ d.f. ££ STA 2023 c D.Wackerly - Lecture 23 0 (2.571) 2.977 (3.365) or (table value)(standard error) ¢ 323 £ STA 2023 c D.Wackerly - Lecture 23 $ £ §¦ # § $ ¥ # ¥ ¥ £  ¢¦  ¢  ¡ !  £ ¨ © ¡ "# $# $ % &  ¤¥ ¢  ¡ 324 9 and confidence. paired difference test? Why did we analyse the data using the 9 The manner in which the data was collected dictated the method of analysis 9 325 milliliters of – MORE information in CI, no more work!!! mercury with – Between CAN tell how big the difference is from the CI difference at the (and others) level. Can’t tell from hypothesis test. CAN say there is A before and after learning biofeedback? © @ . 326 , controlling for the others by collecting the data in this manner!!! Can assess the impact of 9. Etc. 8. Ethnic background 7. Gender 6. Stress level 5. Lifestyle 4. Weight of patients 3. General physical condition 2. The age of the patients 1. Learing biofeedback measurements? What “factors” could have an impact on the BP Why were the data collected this way? STA 2023 c D.Wackerly - Lecture 23 Is there a “big” difference in the mean BP readings £¢ © ¡ STA 2023 c D.Wackerly - Lecture 23 ¡ ¦  ¡ ! 9 Stat 9 Paired Click in box labelled ”First”, double click on Basic Statistics Minitab? Punch in data values $ Click in box labelled ”Second”, double click on Variable 1 (Before in this case). 9 Click Options, type in confidence level (for CI) Variable 2. (After in this case) 9 Click OK, OK. value 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 SE Mean 8.98 6.79 3.43 327 P-Value=0.015 Choose alternative (Greater than in this case), null 9 Kelly Sodec Mathew Smeltzer Pavlina Rumcheva Terry Mashtare Saurabh Kumar Donte Ford David Finlay Adam Glassman David Ashley Shamshad Ali Instructor Sections 328 CAR 100 TUR L007 TUR L007 McC C 100 CSE A101 CSE A101 McC C 100 CAR 100 CAR 100 CAR 100 Location Final Exam Wednesday, May 1, 10:00 am – 12:00 noon Conflicts – see Wackerly NOW STA 2023 Final Exam Locations STA 2023 c D.Wackerly - Lecture 24 STA 2023 c D.Wackerly - Lecture 23 ¡¢ ¨¡¦ ¡¦ ¡¦ ¡¢ ¡¢ ¡¢ ¦¦ ¡¢ ¡¢ ¤ ££ ¤  ¤ £ ¤ ¡ ¤ ¦ ¤ ¨£ ¥© ¤ ¨ ¤ §¨ ¥¡£ ¤ ¤ ¡¢ ¡¦ ¡¦ ¡¨¡ ¡¦ ¡¦¡ ¡¢ ¡¦ ¡¦ ¢¡¦ ¤¤ ¥©£ ¥¡£ ¤  ¤  ¤ £ ¥¡ ¤  ¤ § ¥©© ¤ £ ¤ ¤ ¡ ¡ ¡ ¡¦ ¡¦ 9 ¡¦ ¡¢¡ ¡¡ ¡¢ 9 ¢£ ¡¦¡  £ ¡¡£ ¡¡ ©¦¡ ¦¡£ § ©§  Confidence Interval: Test Statistic: DIFFERENCES Method of Analysis : do a one-sample “t” ON THE Assumptions: Differences appr. Normally dist. Last Time : Paired-Difference Experiments problems on syllabus! 9.60, 9.97, 9.100, 9.107 and rest of Chpt 9 For Thursday : Exer. 9.46, 9.52–54, 9.56, 9.59, estimator (table value)(standard error) male managers, from Fortune 500 corporations. women. of females managers married. of the male 330 (Male = “1”, Female = “2”). female managers who are married. Find a 95% CI for difference in proportions of male and managers married, female managers Ex. # 9.54, p. 407 Managerial careers of men and STA 2023 c D.Wackerly - Lecture 24  ¢ ¡  ¢ ¡ Today : p. 402 – 406 329 ¤ £ " ¤ £ " Assignments # £ STA 2023 c D.Wackerly - Lecture 24 $ £ ¤ ¤ ¤ ¥¤ ¥ $# % & ¥ ¤ @ ©£ £  ¤   ¤ 1 0 ¥ ¥ ¥  © ¡¨¡ @ § £ £ from pop 2,   9 from pop 1, ¡  9 6¡  ¢ ¡ ¤ ¤ attribute attribute Independent samples: Pop 2 Pop 1 Have: Two populations Independent Samples (p.402) Comparing Two Population Proportions # with attribute estimates estimates estimates # with attribute (p. 402) (p. 402) are large. (p. 402) is approx. normally dist’d when both ¡  ¢ ¡  ¢ ¡   7¡ ¡ £ ¡ 6¡ 9 ¤  ¡ 7¡ ¡ ¡ ¢ ¤ ¦  £ ¡ ! ¤ £ " ¤ £ "  ! ££ " " ££  ¢  ¡ ¡ ¡ ¢ ¡ ’s 331 STA 2023 c D.Wackerly - Lecture 24 Large Sample estimator formula sheet  ¢ ¡ standard errors (P. 403) table CI for formula sheet male managers, from Fortune 500 corporations. women. of females managers married. of the male 332 (Male = “1”, Female = “2”). female managers who are married. Find a 95% CI for difference in proportions of male and managers married, female managers Ex. # 9.54, p. 407 Managerial careers of men and   ¢ ¡  ¢ ¡ ¡ § ¨© ¤ £ " ¤ £ "  £  ¡ ©£ @ £ § ©£ ¤  ¡ ¤   © ¡¨¡ @ § ¤  £ £ STA 2023 c D.Wackerly - Lecture 24 ¤  #  ¤ §  ¢ ¡ ¤  © ¡¨¡  ¢ ¥ ¦ # !  ¢ ¡  !  £  ¡ ¤ ¦  % & ¥ ! ¢ ¨© § %  &  ¨©  @ © £¢ £ £ and female managers who are married by between managers who are married exceeds the proportion of At the confidence level , the proportion of male @ ©   ¢ ¡ !  ¢ ¡ # ¥ #  ¢ ¡ ¡ £¢ # © ©¡ ¥ % & ¡ ¤ % & ¢ ¢  ¡ ¥  ¢ £ £ ¢ £ § versus  ¡ ¡ ¡   ¤ ¦ ¨ 1 ¡ § OR OR ¡ ¡ ¡ ¨ £ ¡ £ ¢  334 RR or score score (tail area) smaller larger p-value a fixed particular value of difference Consider testing (p. 404) ¢ £ ¡ £ 0 0 0 ¡   ¦ STA 2023 c D.Wackerly - Lecture 24 ¥ Confidence interval: 333 0 ¢ ¢ ¢ ¥   ¥ ¥ ¥ ¥ £ ¥ % £ ¡ ¥ % % & % & ¥  STA 2023 c D.Wackerly - Lecture 24 ¢  ¥ ! ! , estimate this total sample size total # “S” in experiment with on formula sheet. 335 NULL HYPOTHESIS , then £ standard error ¡ hypothesized value , use the individual ’s COMMON value of If If ¢ ¢ £ ¡ ¡ ¥ ¢ standard error ¡ ¡ ¡ ¡ ¡ ¢ Formula Sheet estimator £¢ £ £ ¡ £ ¥ 00 £ ¡ ¡ £¢ ¢ ¤£  " ¤¦ "¦  ¢ ¦( ¤  ¤¦ ¦ (  ¢ ¡ ¤ ¡  ¢  ¡ ¡  ¦ ¢ 0  )  ¡ ¤ ¢  ¡ £ £ ¢ ¡ ¡ !  9 336 Use . of true prop. of premi’s given inositol with eye on standard diet had eye injuries. compensate for poorly developed lungs eye injury to to high oxygen levels used to of Is ? tail test, eye injuries RR : true prop. of premi’s not given inositol with injuries (2) (1) premature infants given inositol had an reduce the risk of eye damage in premature infants? Ex. : # 9.107, p. 431 Does inositol (found in breast milk) STA 2023 c D.Wackerly - Lecture 24 9 9 TEST STATISTIC 9¦ 9 9  9  ) ¡ ¡ STA 2023 c D.Wackerly - Lecture 24  ¡ ¦ £  § £ ¢ £ £ 0 ¡ ¦ £ £ ¦¢ ¢¦ ¢¦ ¡ ¨ ¡ § ¡ ¡ £ ¡ ¨ 1 ¤£  " £ ¢ ¤¦ "¦ £ £  ¡ ¦ £ ¡  ¤ £ © level, there P-value : Lower tail test – oxygen levels for infants given inositol. of premature infants with eye injury due to high evidence to claim a lower proportion Decision : at the Test Statistic ¥ ¢ £ ¥ £ £ ©¨ ¢ ¤ ¡  ¡ ¦( ¤¦ ¦  0 ¢ ) 9 9 p-value 9 337 -value larger than , claim a lower 338 significantly lower for any proportion with breathing irregs if given inositol. Not For any STA 2023 c D.Wackerly - Lecture 24 – Claim – Claim – ? ? ? STA 2023 c D.Wackerly - Lecture 24 ¢¢ ¡ £ ¢ £ 9  9 9  ¢¢ 9 £¢ £ £ ¢¢ £ © ¦¢ © £ ©¦ ©¦ Stat 9 Basic Statistics 2-Proportions Minitab? Click Radio button “Summarized data” STA 2023 c D.Wackerly - Lecture 24 ”First Sample” in box labelled ”Trial”, type in # of 9 339 ”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” 9 Click ”Options” type in # successes (29 in Ex 9.107). trials (110 in Ex 9.107), in box labelled ”Successes” 9 Choose alternative (Less than in Ex 9.107) 9 Click in box ”Use pooled estimate for p for test”. 9 Click OK, OK 9 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 9 ...
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This note was uploaded on 12/15/2011 for the course STA 2023 taught by Professor Ripol during the Spring '08 term at University of Florida.

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