Week12-4up - 273 STA 2023 c D.Wackerly - Lecture 20 STA...

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Unformatted text preview: 273 STA 2023 c D.Wackerly - Lecture 20 STA 2023 c D.Wackerly - Lecture 20 274 Last Time : Tests and Confidence Intervals for a based on SMALL samples. ¡ Population Mean, ¢ Assumption : POPULATION approx. NORMALLY dist. :  ¨¦£ ¤   ©§ ¥ ¢ ¢ Hypothesis Tests ¡ Confidence Interval for " '¡ $ " (&%¡ #! versus ¡6 87¡ "0 ¡E 87¡ ¡ H$ PI¡  © § 6 §  F Q© § GE § RR OR Monday : P. 378 – 383 (rest of Sec. 9.1) For Tuesday: Exer. 9.7, 9.16, 9.17, 9.95, 9.105, 9.114 OR 275 ¢ 276 © Q§ V W '  UF £ ¤ $ § ¡ (looks just like !!) (like before) AND #d.f. From the table, ¢ $ Qppvh5 eGE § A9 Dht a F @ ¢ $ ucqgf5 r6 § A9 $ Qpqgf5 erE § A9 Dts a @ Dts a F @ ` ) depends on ¢ X § © Y¢ (new) (tail area) STA 2023 c D.Wackerly - Lecture 20 Test statistic : (and or STA 2023 c D.Wackerly - Lecture 20 p-value S TR 8.117, 9.1, 9.13, 9.19, 9.22, 9.24, 9.25 F © § GE § For Thursday: Exer. 8.49(c), 8.54(c), 8.106(c), 107, ©§ 6 § P. 374 – 383 (Sec. 9.1, “Large Sample”) calc. value of 20 D 4)CB) § E § A9 @ Today : P. 343 – 345 (p-values), $ 4)31§ 20) Assignments Small Sample (p. 292): D 20) @ 34)CB§ 6 § A9 readily if you tell them that Benjamin Franklin said it first. From the table, ¢ Table does not allow us to get exact p-values. Thus, in this case, best we can say is that Can’t be any more precise using these tables! w $ w w w w w and aa pb$ are ) to R qgf5 a h Closest values in table ( with d.f. $7` $7` $7` $7` $7` $ 7` ¢ R igf5 ed$ § h aF Look at table, h €5 xc€ 5 t €5 ‚ p€ 5 € a 5 x ya 5 , ¢ p-value aa cb$ In Everglades example, lower tail test, d.f. 5 3§ Thought: People will accept your ideas much more Ho . Ho . Ho . Ho . ¢ ¢ 277 STA 2023 c D.Wackerly - Lecture 20 STA 2023 c D.Wackerly - Lecture 20 278 € 5 b$ § t $  a Ex. : New case, lower tail test, d.f. ¢ Closest values to and If d.f. € 5a is if d.f. €€ pa 5 $ uif 5 r6 § @ 9 Dt a x$ 5 a 6 § A9 ¢ @ 5 a 6 § A9 ¢ @ So . STA 2023 c D.Wackerly - Lecture 20 280 Exercise 10.52 Pouring temperature of molten iron. , € a $ D uh ‚ 5 R 6 § A9 @ are 2541 2544 2620 2560 2559 2562 2553 2552 2553 Want : two tailed test Minitab? ¢ E E p-value . Stat Basic Statistics 1-Sample Select variable and click Radio button “Test mean” ¢ ¢ tail area ¢ E ¢ E So Punch in data values ¡ ¢ and ¡ ¢ $ F Ds Qpt a 5 h rE § @ $ D qgf5 R GE § A9 €a b$ A9 ¢ tF@ then . § . measurements 2543 ¢ ¢ and temperature different than target? Use €pxpxpRGH $ ¡ " 0  ¢ h ‚5 R F D uh ‚ 5 R GE § @ 9 in table for d.f. Target setting is 2550 degrees. Actual mean pouring €a b$  Closest values to F € h ‚ 5 R d$ § a $ p-value = And and €x ixcpR $ ¡ "  ¢ ¢ 279 Ex. : New case, two-tailed test, d.f. If d.f. then D€ $ uif Dt STA 2023 c D.Wackerly - Lecture 20 tail area . are a € 5 7` $ ¢ x$ So p-value in table for d.f. in table for d.f. $ F D Qt € vh5 R rE § @ $ D € t ‚ 5 eGE § @ 9 aF ‚ &$ A9 ¢ Closest value to € a 5 R ¢ ¢ p-value = , ‚$ @9 ¢ p-value = D $ d.f. , €F a 5 R d$ § ‚ $ Ex. : New case, upper tail test, Select Alternative, Type in Null Value, OK T-Test of the Mean . Test of mu = 2550.00 Variable C1 N 10 vs Mean 2558.70 mu not = 2550.00 StDev 22.75 SE Mean 7.19 T 1.21 P 0.26 ¢ 281 282 Ex. Investigation between “handedness” and motor ? competence in preschool children. Scores on motor skills tests.  Left-handed (1) 41 97.5 17.5 Right-handed (2) 41 98.1 19.2 temperature differs from 2550 at the .01 level of Minitab CI? 1-Sample § ¡ Basic Statistics Find a preschoolers. ¡ ¢ Samples from two populations ¢ SE Mean 7.19 HOW???? 99% CI (2535.32, 2582.08) STA 2023 c D.Wackerly - Lecture 20 283 StDev 22.75 ¢ Mean 2558.70 Objective is to compare two means mu not = 2550.00 STA 2023 c D.Wackerly - Lecture 20 Large Sample Inferences about Differences If both populations normal, then ¢ If and  ¡ Independent Samples (Section 9.1) ¢ Between Two Population Means, 284 “large”, then normal. approx normal, regardless of shapes of sampled populations. Independent samples from two pop’s. (P. 375)  ’s, use them, otherwise use   © X ¥ D  £ ¤ F ¡ £ ¤ @  £ Know ’s  [formula sheet, P. 375] formula sheet   £¤ F ¡ £¤ [formula sheet, P. 375] table ¡ £   ¡ £ 9 86 5 7 formula sheet standard errors  estimator 7 5 9 @6 5  @ © X ¥  £¤ ¡¡  UF ¤¡ (p. 375) large. 7 @6 ¡ ¡  – Use the difference in sample means, and 5 D9 ¡ .    £¤  Want: Estimate for  Sample variance Both ¡ Sample mean Large Sample CI for (p. 376)  Sample size ¡£ ¡ ¢¡ Pop. variance £  ¡ Pop. mean Pop. 2 (& $ "   )'%#!¤ ¢ Pop. 1 1 20 ¢ T Confidence Intervals Test of mu = 2550.00 vs " ¢ Type in Confidence Level OK 3 40 ¢ interval” N 10 confidence interval for the true difference in mean motor skills scores for left and right handed Select variable and click Radio button “Confidence Variable C1 €s Stat significance. £¤  GF ¡ £ ¤  £¤ F ¡ £¤ ¢ claim that the mean pour £¤ ¢ Is STA 2023 c D.Wackerly - Lecture 20  ¢ Conclusion at .01 level? STA 2023 c D.Wackerly - Lecture 20  £   ¡ ¡ £ $   ¡ ¡¡  UF ¢P$   ¨ ¥§ ¥ § ©¦¡   ¨ ¥§ ¥ § ©£ ¢ ¡¢ 97.5 £¤ 17.5 Right-handed (2) 41 98.1 19.2  ¡¢ What does it mean if ¢ by than equals ? equals by ? How can we interpret the 90% confidence interval, D t¢ 5 pf € 5 £f R f F @ , for the difference in mean motor skills $ ¡ ' &$ Q© X X  scores for left and right handed preschoolers? (the true mean dexterity score for left-handers) ¢ ¡ ¢¡  could be as much as larger than (the   true mean dexterity score for right-handers) . (the true mean dexterity score for left-handers) ¡ ¡  $`   Q© X ¥ D  £ ¤ F ¡ £ ¤ @  ¥ could be as much as ¡ ¡¢ ¡ smaller than $ uvt5 t ¥ f (the true mean dexterity score for right-handers) . ¢ 287 STA 2023 c D.Wackerly - Lecture 20 or anything in between. STA 2023 c D.Wackerly - Lecture 20 288 Consider testing (p. 376) or S TR ¤ H $  UF ¢¡ ¡¡ (tail area) TEST STATISTIC hypothesized value standard error w pw NULL HYPOTHESIS     ¡¡    F  ¤ F ¡ ¤ ¤ § ¥ $X Formula Sheet ¥ F estimator ¥ ¦¥  £  ¡ ¡ £   F  ¤ F ¡ ¤ $ X ¤ w ¢ preschoolers by 7 points? 6 Q© X AX  F E © X G¦X ' handed preschoolers is larger than the mean for RH E  UF ¡ ¡ ¡ Is it plausible that the mean dexterity score for left ¤ ¢ RH preschoolers by 5 points? OR ' handed preschoolers is smaller than the mean for OR FE © X G¦X ¢ Is it plausible that the mean dexterity score for left p-value 20 E D 4)CB) X ¦X @ 9 €s preschoolers by 5 points? RR 6 © X ¦X handed preschoolers is larger than the mean for RH calc. value of D 20 6 34)CB) X ¦X @ 9 ¢ Is it plausible that the mean dexterity score for left versus $ 4)C1) X 20 confidence level. a fixed particular value of difference X be ' ¤ 6  UF ¢¡ ¡¡ "0 " $  ¡ y¢¡ "  F¡ left and right handers. This claim ¤ Claim : no difference in mean dexterity scores for ' €s preschoolers. ¡ mean motor skills scores for left and right handed is ¡ ¢¡ confidence interval for the true difference in rejected at the is ¡  41 90% CI is than What does it mean if Left-handed (1) Find a is ¡ skills tests. ? f R Qf F 5 competence in preschool children. Scores on motor equals € What does it mean if 286 ¡ ¡¡  UF ¤¡ ¡ ¡¡  UF ¤¡ ¡ ¡¡  UF ¤¡ Ex. Investigation between “handedness” and motor STA 2023 c D.Wackerly - Lecture 20 f €5 t 285 STA 2023 c D.Wackerly - Lecture 20 ¢ ...
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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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