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Unformatted text preview: 217 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 218 Last Time:
to within “B” units with £© § ¥ £
¨¦¤¢ ¡ Estimate conﬁdence.
and solve for . (p. 307)
2 0(
1)' %#!
$& " Thought: Eagles may soar, but weasels aren’t sucked Parts of a statistical test. (p. 322) into jet engines. 3 The hypothesis of MAIN INTEREST is the
ALTERNATIVE or RESEARCH hypothesis, –
5
64 light bulb ex. , ©GFE£ B ¡9 5 4
AADCA@87¢ Assignments . (p. 322) What we are “trying to prove” in an objective, fair
Today : P. 328 – 332 manner
3 The “other” hypothesis is called the NULL For Tomorrow : Exercises 8.18, 8.21–23, 8.25, 8.27 , light bulb ex. (p. 322) ©GFE
AA£ ( ¡9 H 4
AP8I¢ Tuesday : Exercises 8.29, 8.33, 8.34, 8.38–41, 8.59, H
64 HYPOTHESIS, –
Monday : P. 334 – 338, 347–351, Errors: p. 325 8.61, 8.67–69 Reality
Decision Correct Type II error Reject Ho Type I error Correct 219 Ha true Accept Ho STA 2023 c B.Presnell & D.Wackerly  Lecture 19 Ho true STA 2023 c B.Presnell & D.Wackerly  Lecture 19 220 Parts of a Statistical Test (p. 326) . 3. Test Statistic : (TS) (p. 325) 3 computed from the sample data using a formula
3 forms the basis for our decision. R
T true
a H
64 V when 5
d4 ©
© Type II error X
§ 3 Q
1(
¢ § 5
64 R
S3 Q
1(
¢ X
YR accepting . 2. Alternative Hypothesis : LEVEL of the test. and/or 4 1. Null Hypothesis : (p. 323), SIGNIFICANCE H Type I error 3 VT
WU§ 3 `Q
@1(
§ 4. Rejection Region : (RR) 3 Then `
@Q `Q
@1(
§ 3 Compute value of TS
3 GFE£ B
Acb¡ R § for the Get data Make decision ’s
3 ¡ 3 The test that we will discuss have the SMALLEST Do experiment
3 ( when aGFE
AA£ saying depends on the choice of ’s that we pick. e
f§ a 3
§ In our lightbulb example, gives values of TS for which H
d4 (
3 saying what we “want” to say when we should not is REJECTED 221 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 222 Decision :
3 If the value of the TS is in the REJECTION
and
4
5 H REGION, we . 4 3 If the value of the TS is NOT in the REJECTION
REGION, we DO NOT REJECT.
because we usually do Courtroom Analogy not know the probability of making an error if we
3 H
84
4 do so.
3 , what kind of error could we : guilty 3 Put burden of proof on Prosecutor : Experimenter 4
H 3 Proof “beyond a reasonable doubt” : – What is the probability of a TYPE II error? small. 4 usually 5 depends on the value of the parameter in § make? Experimenter : Prosecutor
3 – If we accept : innocent
5 H
64 – We do not ACCEPT that is really true H
64 Don’t want to accept , so we reserve judgement 223 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 224 Large Sample Hypothesis Testing ¤ ¦§ (
H¡
( ¨¤
( ¨¤ ©¥
¦ ¥ H¡ 2
2
§ ¦ ©¥
¦ ¥ H 4 3 GFE
A£ H¡ ©¥ ¦ ¥ ¨¤
( ( ¡
A9 H GFE£ B ¡
ADCA9
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84 5
64 5 4
4
(H¡ 3 3
3 has a ¥ ¡
A9 B¡
bA9 ¡9 H
AP84 Test Statistic, TS
§ ¦ ( is true, H¡ H¡ ¨¤ is a TEST STATISTIC
If 2 ¨¤ ¡
%¥ is true . Need Rejection Region, RR § ¦
¨¤ 3 ( H¡
H¡ ¡
3 ¡ if ¡
%¥ ¥ (
¡ is a distribution 2 ¥¦
( ¡ 3 In this case, has an APPROXIMATE That is Lightbulb Example : 2¢ a ﬁxed particular value of ¢
£ Recall : Large Sample ©
E about a Population Mean, distribution § 2
(
B 9
9 5 4 ¦
§¦
¢
£¡ H¡ H¡ (
¡ “Upper Tail test”, “One Tail Test” (p. 329) in favor of ¡ ¡
A9 H 3
3 4 ¡
A9 4
H ( ¥
¤
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£ ¨
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2 ( F e E
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§
( STA 2023 c B.Presnell & D.Wackerly  Lecture 19 228 AT THE 4
5 in favor of printed circuit boards claims that “product can inspect,
“refute the claim” based on data for
onesecond runs? Use . level of
and ?
9H
P84 3 H
84 G
e ( G
A e §
G ( £ e 95
@84 § – RR :
If we are interested in : 2 ¦ 9 ¦
§¦
9 £ e GFE
AA£ conﬁdence ). level” ( or ( £ e H
84
with at the § ¡9 5
A@84 bulbs is larger than ¡
%¥ ¢
¨ ¤ £¡
claim that the mean lifelength of all H¡ “ ¥ ¤ 2 §
¡ %¥ – In terms of this problem ¨¤ ¡9 H
AP84 ( level ? ( G e£ at the B – E
E e F – Conclusion : Is H¡ 3
3 GFE
£ conﬁdence ). 5
84 3 signiﬁcance” ( or with ¡ at the , is § 3 “ Claim that the mean lifelength of all bulbs, G
A e Q In terms of this problem: ( ` 4
H on average, at least 10 boards per second”. Evidence to LEVEL!! 2 3 Ex. : #8.24, p. 333 Manufacturer inspection equip. for Conclusion : ¨
( 5
84 3
227 ( (
B B¡
CA9 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 G
A e 4
5 ¡ zα level test, RR : E
E F (
§ 5
64 Data : GFE£ B ¡
AcbA9 B¡
CA9 3 α ( ¡ ¤ Rejection region : GFE
A£ 3 ¡ “something” type I error 0 true mean lifelength of ALL BULBS
( Rejection region : If we wanted B¡
bA9 . Ex. : Lightbulb Example If we are interested in Want than H¡ Should is probably 2
¥
§ ¦
¤ %¥ ¤
¡
¨ The true value of by a “lot” of standard errors. ¨¤ than ¥ ¤ is ¡ ¡ is POSITIVE and LARGE 226 4 If H true value is. ¡
A9 , whatever that ( is close to the true value of STA 2023 c B.Presnell & D.Wackerly  Lecture 19 H¡ FACT: 225 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 α – NOTE: This DOES NOT mean that
is true!! − Zα 0 “Lower Tail test”, (p. 329) GF
AE £ ( ¡
A9 4 3 STA 2023 c B.Presnell & D.Wackerly  Lecture 19 229 Back to #8.24:
3 Data:
10 9 10 10 11 9 12 8 7 10 11 9 9 13 9 10 9 9 9 7 12 6 9 10 11 12 10 0 10 11 12 9 8 9 6 10 11 10 12 8 10 8 7 9 7 9 9 10 ¤ F e ©(
( E
A£ e F ¥
F (
V level test 2 ( G
A e
( ( level of signiﬁcance. In terms of this e E e F ¥
E 3 e ¥ at the ¨
E e G
A e application: “There ( 3
§ RR : enough evidence at the level to indicate that the mean number of circuit G
A e boards inspected per second is less than 10 .” 3 ...
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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.
 Spring '08
 Ripol
 Statistics

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