Week12-2up - 8.61, 8.67–69 Tuesday : Exercises 8.29,...

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Unformatted text preview: 8.61, 8.67–69 Tuesday : Exercises 8.29, 8.33, 8.34, 8.38–41, 8.59, Monday : P. 334 – 338, 347–351, For Tomorrow : Exercises 8.18, 8.21–23, 8.25, 8.27 . (p. 322) HYPOTHESIS, – Ho true Correct Type I error Accept Ho Reject Ho Correct Type II error Ha true Reality Decision Errors: p. 325 (p. 322) , light bulb ex. The “other” hypothesis is called the NULL manner ¢ Today : P. 328 – 332 , 218 What we are “trying to prove” in an objective, fair light bulb ex. ALTERNATIVE or RESEARCH hypothesis, – The hypothesis of MAIN INTEREST is the '( ¦ Assignments and solve for Parts of a statistical test. (p. 322) ©  confidence. . (p. 307) to within “B” units with $ ¡  £& )! ) #! into jet engines. Estimate " #! ¢ "! $ ¡ % £& Last Time: STA 2023 c B.Presnell & D.Wackerly - Lecture 19 § ¦ Thought: Eagles may soar, but weasels aren’t sucked 217 '( STA 2023 c B.Presnell & D.Wackerly - Lecture 19   ¡   £¢  ¥ £¦ ¤ ¨ § ¥ LEVEL of the test. Type I error ¥ ¥ ¥ Type II error when true when ’s that we pick. The test that we will discuss have the SMALLEST saying '( In our lightbulb example, for the 219 saying what we “want” to say when we should not accepting and/or (p. 325) (p. 323), SIGNIFICANCE ¡  £& ¡  £ ¤¢  ¦  ¥ § STA 2023 c B.Presnell & D.Wackerly - Lecture 19 '( ¥ ’s . forms the basis for our decision. Make decision Compute value of TS Get data Do experiment depends on the choice of gives values of TS for which 4. Rejection Region : (RR) Then . 220 is REJECTED computed from the sample data using a formula 3. Test Statistic : (TS) 2. Alternative Hypothesis : 1. Null Hypothesis : Parts of a Statistical Test (p. 326) STA 2023 c B.Presnell & D.Wackerly - Lecture 19 )!  ¢ ¡ ¥ ¦  § ¦ ¥ ¡ ¢ ¦ ¢ ) #! ¦ £¥ "! % £& ¡ § ¡ "! ¨ ©¥ )! and . 221 because we usually do , what kind of error could we judgement Don’t want to accept usually that is really true , so we reserve depends on the value of the parameter in )! – What is the probability of a TYPE II error? make? – If we accept do so. )! not know the probability of making an error if we – We do not ACCEPT )! REGION, we DO NOT REJECT. If the value of the TS is NOT in the REJECTION REGION, we ) #! If the value of the TS is in the REJECTION Decision : "! "! : innocent Courtroom Analogy STA 2023 c B.Presnell & D.Wackerly - Lecture 19 Proof “beyond a reasonable doubt” : small. Put burden of proof on Prosecutor : Experimenter Experimenter : Prosecutor : guilty )! "! STA 2023 c B.Presnell & D.Wackerly - Lecture 19 ¥ 222 "! )#! $ ¡ a fixed particular value of "! $ Rejection Region, RR Test Statistic, TS Need In this case, )¡ )! Lightbulb Example : $ ¡ %  )¡ )¡  $ ¡  £& . % £& STA 2023 c B.Presnell & D.Wackerly - Lecture 19 has an APPROXIMATE Recall : Large Sample ¢ ¡ is true has a If is true, is a TEST STATISTIC if is a That is )! ) #! '( ¡  about a Population Mean, 223 ©  '( ¡ £¤  )¡ ¡ $ ¢¦  ©  ¢¦ ¢¦ Large Sample Hypothesis Testing ¡ ¢ £ ¨¤ § ¤ £ ¨¤ § £ ¨¤ § £ ¡ &  ¤ ¥  ¡ ¤ )¡ ¤ )¡ ¤   STA 2023 c B.Presnell & D.Wackerly - Lecture 19 ¢¦ §¦ ¢¦ ¤ © 224 distribution distribution © © ¢¦ ¤ ¤  ¡ ¥  ¤ )¡ ¥  ¤ )¡ ¥  Should © Rejection region : If we are interested in 0 zα α type I error © Rejection region : Want ¦ “something” in favor of than . by a “lot” of standard errors. is probably than The true value of is is POSITIVE and LARGE $ ¡ % ¡ ¡ If ¢ "! ¡ ¢ true value is. )¡ ) #! $ " #! $ ¡ § % , whatever that true mean lifelength of ALL BULBS Ex. : Lightbulb Example “Upper Tail test”, “One Tail Test” (p. 329) Data : © is close to the true value of ¥ % ¢ ¡  §( ¡  ¡ FACT: level test, RR : ¢ ¡ STA 2023 c B.Presnell & D.Wackerly - Lecture 19  £& )! "! ¥ ¡ ¡ $   "! $ ¡ ¤ $ © $ ¦ § ¨  § 225 ¤  £  & )¡ )#! $ ¡  £& % £& § '( '( & ¨ ¡ © %  © $ ¥  )¡ )¡ % '& ' ¥ © ¢¦ ¤ © ¢¦ ¤ ¤ ¡ ¥  ¡ ¥  & § STA 2023 c B.Presnell & D.Wackerly - Lecture 19  226 )! ¥ §( ¨ ¥ ¨ at the level level of confidence ). at the is true!! level” ( or claim that the mean lifelength of all ? , is AT THE confidence ). at the – NOTE: This DOES NOT mean that with § bulbs is larger than “ – In terms of this problem – – Conclusion : Is – RR : If we wanted ) #! § '( £& significance” ( or with § & % §£ ¨ § ¨ “ Claim that the mean lifelength of all bulbs, In terms of this problem: LEVEL!! in favor of "! 228 and α − Zα If we are interested in : ? one-second runs? Use 0 . “refute the claim” based on data for on average, at least 10 boards per second”. Evidence to printed circuit boards claims that “product can inspect, Ex. : #8.24, p. 333 Manufacturer inspection equip. for "! )! $ ( £& Conclusion : ¥ §( ¨ ( ¨ '( ¥ ¡ STA 2023 c B.Presnell & D.Wackerly - Lecture 19 ¡ &' §£ ¨ "! )! $ $ ¢  ¥ ¡ ¡ © $ ¡ “Lower Tail test”, (p. 329)  §£ ¨ 227 © "! $ STA 2023 c B.Presnell & D.Wackerly - Lecture 19 ¤ © £ '( ! £ §( ¨  )¡ )¡ ¢¦ ¤ ¨ $ ¡  £& ¤ ¡ ¥ ¦ ©  ¢¦ ¤ )! $  ¡ ¥  10 8 11 9 7 RR : 10 11 9 10 6 7 9 10 9 12 9 8 at the 9 10 0 7 9 10 7 11 10 12 9 11 9 10 11 6 13 9 9 12 12 9 9 12 10 8 9 10 10 8 229 enough evidence at the boards inspected per second is less than 10 .” level to indicate that the mean number of circuit application: “There level of significance. In terms of this level test £ 10 ¢ Data: §  Back to #8.24: ¤ STA 2023 c B.Presnell & D.Wackerly - Lecture 19 § ' ¨  ¨  £' ¥ §( & ¨   © '  ¨ §( § ¨¤ &  §( ¨ ¦ § & ¨¤ § § ¨ &' ¨ ...
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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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