Week12-2up - For Tuesday: Exer. 9.7, 9.16, 9.17, 9.95,...

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Unformatted text preview: For Tuesday: Exer. 9.7, 9.16, 9.17, 9.95, 9.105, 9.114 Monday : P. 378 – 383 (rest of Sec. 9.1) 8.117, 9.1, 9.13, 9.19, 9.22, 9.24, 9.25 For Thursday: Exer. 8.49(c), 8.54(c), 8.106(c), 107, P. 374 – 383 (Sec. 9.1, “Large Sample”) Today : P. 343 – 345 (p-values), Assignments readily if you tell them that Benjamin Franklin said it first. Thought: People will accept your ideas much more 273 ¢ Population Mean, ¢ based on SMALL samples. Last Time : Tests and Confidence Intervals for a STA 2023 c D.Wackerly - Lecture 20 Hypothesis Tests Small Sample (p. 292): Confidence Interval for dist. versus OR OR : Assumption : POPULATION approx. NORMALLY ¡ 2 STA 2023 c D.Wackerly - Lecture 20 ¡ ¡ ) ¡   ¡ ¡ % !  ¡ ¦ ¡ ¢ ¡ ¦ 0 1) ¦ RR or (tail area) p-value calc. value of ¦&' ¦&' 543  ¦ 0 1) %¦  %¦  )¦ ¡ %¦ § ¦ § ! " ! " ¦ ! "  § ©¨ ¦ £¤ ¦¥ § ©¨   § ©¨ # $¦ ( ( 274 ¢ ¢¦ § In Everglades example, lower tail test, d.f. Table does not allow us to get exact p-values. ¦  0 and Closest values in table ( with d.f. are Look at table, p-value ¢ ¢ £ ¢ ¦  ¦ # ¥ ¤ 3 ¢ ¢ 0 £¤  § ©¨   ¡  275 ) to , From the table, STA 2023 c D.Wackerly - Lecture 20 £ Can’t be any more precise using these tables! Ho . Ho . Ho . Thus, in this case, best we can say is that Ho . From the table, ¢ (new)  ¤ ¦ ¢ ¦&' ¨ ¨ ¨ ¨ ¨ ¨ ¢  # ¢  # ¢  # ¢  # ¢  # ¢  # £© £ © (like before) AND #d.f. £ § ( ¦&' ¢ ¥ ) depends on £ £ 0) #      § # (and £ § ¢ £ (looks just like !!) £ #% ¥ ¡  # ¦&' 0 1) ¤ ¦ Test statistic : £ §¥ ( STA 2023 c D.Wackerly - Lecture 20 ¥ ¤ 3 ( 276  #% £ ¦&' #% ¢ ¢ ¢ ¢ ¢ ¢ ¤ if d.f.  is ©  ¦&' ¦&' § ( in table for d.f. ¤ # ( (  § ( £ £ #% So p-value  £ § ¦  # © # If d.f. Closest values to p-value = So and then , . . in table for d.f. Ex. : New case, lower tail test, d.f. ¢ ¢ ¢ ¢ Closest value to  ¦&'  0) p-value = ¥  3 # d.f. § &'  £  STA 2023 c D.Wackerly - Lecture 20  , 277 £ Ex. : New case, upper tail test, £   #  ¦ STA 2023 c D.Wackerly - Lecture 20 § 3 0) # ¦&' ( £ 0  3 and are #   ( £ 278 If d.f. Closest values to tail area ¢ ¢ So And 0) then and . 3 p-value tail area . . in table for d.f. 279 and are ¥ 2559 2543 2562 2541 2620 2552 2544 2553 measurements temperature different than target? Use 1-Sample Variable C1 N 10 vs Mean 2558.70 Test of mu = 2550.00 T-Test of the Mean StDev 22.75 SE Mean 7.19 mu not = 2550.00 T 1.21 P 0.26 Select Alternative, Type in Null Value, OK Basic Statistics Select variable and click Radio button “Test mean” Stat Punch in data values Minitab? Want : two tailed test 2553 2560 . Target setting is 2550 degrees. Actual mean pouring Exercise 10.52 Pouring temperature of molten iron. STA 2023 c D.Wackerly - Lecture 20 p-value = £ ¢ ¦&' ¥ # ¢ 0) £ ¥ £ ¦ , ¥ Ex. : New case, two-tailed test, d.f. ¤ 0 £ ( STA 2023 c D.Wackerly - Lecture 20 § # §¦ ©  ¦&' # (  ¢  3 # 3 #%  ( 2 ( ¥ 0) # © 3  )  3 ) ¦&' ¢ 3  ¢ ¢ ¦&' )  ¢ 3 ) © ¦ £ ¢ ! ¢   ¡  ¡ © ¢  # ¢ £ 280 ¢ ¢ claim that the mean pour ? Basic Statistics 1-Sample Minitab CI? Variable C1 N 10 Mean 2558.70 T Confidence Intervals Test of mu = 2550.00 vs StDev 22.75 SE Mean 7.19 mu not = 2550.00 Type in Confidence Level OK interval” 99% CI (2535.32, 2582.08) Select variable and click Radio button “Confidence Stat significance. temperature differs from 2550 at the .01 level of Is Conclusion at .01 level? 281 98.1 19.2 17.5 282 confidence interval for the true difference in 41 Right-handed (2) 97.5 Samples from two populations preschoolers. mean motor skills scores for left and right handed Find a 41 Left-handed (1) skills tests. competence in preschool children. Scores on motor Ex. Investigation between “handedness” and motor STA 2023 c D.Wackerly - Lecture 20 ¦ ¢ ¢ ¢  STA 2023 c D.Wackerly - Lecture 20 ¢  Objective is to compare two means HOW???? ¢ ¦ £¤ ¢ ¢  Sample variance Sample mean Sample size Pop. variance Pop. 1 . Pop. 2 (p. 375) [formula sheet, P. 375] [formula sheet, P. 375] – Use the difference in sample means, ¡ ¢ ¢ Pop. mean Want: Estimate for ¤£ ¢ ¤¢ ¡ ¤¢  ¤¢  If both populations normal, then STA 2023 c D.Wackerly - Lecture 20 “large”, then (P. 375) Know Both large. estimator and Large Sample CI for (p. 376) formula sheet table standard errors formula sheet ’s, use them, otherwise use 284 approx normal, normal. regardless of shapes of sampled populations. and If © Independent samples from two pop’s. ¥¦ ¥¦ 0¡ © ¡ §  § ¡© ¨  Independent Samples (Section 9.1) 0¡ ¡ ¡ © £¤ ©     Between Two Population Means, ¡ ©© ¡ Large Sample Inferences about Differences ¡© ¡© ©© £¤© © © © ' © 0 £¤ ¢ ¢ ¥  © !" 0 £¤ ¡  # £¤© !" ¥ ( # © 0 £¤ ' § ©¨ ©   !"  © ¡ © ¡ ¨ ¡ © £¤© 0 £¤ £¤© £¤© ©© ’s © § ©¨ ¡   #( # 283  STA 2023 c D.Wackerly - Lecture 20   41 41 98.1 97.5 19.2 17.5 confidence interval for the true difference in Right-handed (2) Left-handed (1) preschoolers. mean motor skills scores for left and right handed Find a ¦ skills tests. competence in preschool children. Scores on motor  90% CI is 285 than by equals equals by than equals ? ? ? How can we interpret the 90% confidence interval, is What does it mean if is What does it mean if is What does it mean if STA 2023 c D.Wackerly - Lecture 20 , for the difference in mean motor skills larger than smaller than or anything in between. (the true mean dexterity score for right-handers) . could be as much as 286 (the (the true mean dexterity score for left-handers) true mean dexterity score for right-handers) . could be as much as (the true mean dexterity score for left-handers) scores for left and right handed preschoolers? ¤ Ex. Investigation between “handedness” and motor ¡ ¤ ¢  ' ¤ 0 £¤ §  STA 2023 c D.Wackerly - Lecture 20 ¥ #¥ £¤© ( ¥ § ©¨ ¡ § § ©¨ §    ¤  ¡   © ¢ ¢ ¡ ¡© ¢ 0' # ( ¤ £¤ © © ¤ ¡ ¡ ¨ © § ¡© ¡ ¢  ¡© 0 0¡ 0¡ ¡© ¡© ¡© 0¡ #  # ¡ ¢ ¤ 3 ¡ ¢3 #£ ¢ ¡© ¡© ¢ ¢ ¢ ¢ confidence level. be preschoolers by 7 points? handed preschoolers is larger than the mean for RH Is it plausible that the mean dexterity score for left RH preschoolers by 5 points? handed preschoolers is smaller than the mean for Is it plausible that the mean dexterity score for left preschoolers by 5 points? handed preschoolers is larger than the mean for RH Is it plausible that the mean dexterity score for left rejected at the left and right handers. This claim versus OR OR Formula Sheet 288 RR (tail area) NULL HYPOTHESIS standard error hypothesized value or p-value calc. value of a fixed particular value of difference estimator TEST STATISTIC ¦  0¡ 0¡ 0¡ ¢ Claim : no difference in mean dexterity scores for ¨  ©¡ ©¡ ¡  0¡  ! ¡ ¡ Consider testing (p. 376) ¡  ¡  ¡©  % ) ©¡    2  ¡ © STA 2023 c D.Wackerly - Lecture 20 ¡ 287 ¨  ¡ 0 ¡  % ¡ ©© ¨ 0¤ ¡ 0) ¡  ¡ 0 1) 0 ¤©  STA 2023 c D.Wackerly - Lecture 20 ¢ 0¤ © %  § ¡ § ©¨ ¡ ¡ 0 ¤© ¨  © © © © ¡ &' &' 543 ¡  § ©¨ ) ! " ¨ ¡ § %  ¡  ¡ ¡ ( !" ( !" ...
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