hypothesis testing variance known?. sampling distribution n over-the-counter stock selling prices...
TRANSCRIPT
![Page 1: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/1.jpg)
Hypothesis Hypothesis TestingTesting
Variance known?Variance known?
![Page 2: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/2.jpg)
Sampling DistributionSampling Distribution
Over-the-counter stock selling pricesOver-the-counter stock selling prices• calculate average price of all stocks listed [calculate average price of all stocks listed []]
take a sample of 25 stocks and record price take a sample of 25 stocks and record price • calculate average price of the 25 stocks [x-bar]calculate average price of the 25 stocks [x-bar]
take all possible samples of size 25 take all possible samples of size 25 • would all x-bars be equal?would all x-bars be equal?
average all the possible x-bars …equals average all the possible x-bars …equals
![Page 3: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/3.jpg)
Levine, Prentice-Hall
Sampling DistributionSampling Distribution
Sample Mean = 5020
H0
![Page 4: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/4.jpg)
Levine, Prentice-Hall
Sampling DistributionSampling Distribution
Sample Mean = 50
It is unlikely that we would get a sample mean of this value ...
20
H0
![Page 5: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/5.jpg)
Levine, Prentice-Hall
Sampling DistributionSampling Distribution
Sample Mean = 50
It is unlikely that we would get a sample mean of this value ...
... if in fact this were the population mean
20
H0
![Page 6: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/6.jpg)
Levine, Prentice-Hall
Sampling DistributionSampling Distribution
Sample Mean = 50
It is unlikely that we would get a sample mean of this value ...
... if in fact this were the population mean
... therefore, we reject the hypothesis that = 50.
20
H0
![Page 7: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/7.jpg)
Levine, Prentice-Hall
Null HypothesisNull Hypothesis
What is testedWhat is tested Always has equality sign: Always has equality sign: , , or or Designated HDesignated H00
• Example ………... HExample ………... H00: : 3 3
![Page 8: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/8.jpg)
Levine, Prentice-Hall
Alternative Alternative HypothesisHypothesis
Opposite of null hypothesisOpposite of null hypothesis Always has inequality sign: Always has inequality sign: ,,, or, or Designated HDesignated H11
Example Example • HH11: : < 3 < 3
![Page 9: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/9.jpg)
Levine, Prentice-Hall
DecisionDecision
Reject null hypothesisReject null hypothesis Retain, or, fail to reject, null Retain, or, fail to reject, null
hypothesishypothesis
Do not use the term Do not use the term “accept”“accept”
![Page 10: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/10.jpg)
Levine, Prentice-Hall
p-valuep-value
Probability of obtaining a test statistic more Probability of obtaining a test statistic more extreme (extreme (or or than actual sample than actual sample value given Hvalue given H00 is true is true
Called observed level of significanceCalled observed level of significance• Smallest value of Smallest value of H H00 can be rejected can be rejected
Used to make rejection decisionUsed to make rejection decision
• If p-value If p-value , reject H, reject H00
![Page 11: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/11.jpg)
Levine, Prentice-Hall
Level of Level of SignificanceSignificance
Defines unlikely values of sample Defines unlikely values of sample statistic if null hypothesis is truestatistic if null hypothesis is true• Called rejection region of sampling Called rejection region of sampling
distributiondistribution Designated Designated (alpha)(alpha)
• Typical values are .01, Typical values are .01, .05.05, .10, .10 Selected by researcher at startSelected by researcher at start
![Page 12: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/12.jpg)
Levine, Prentice-Hall
HoValueCritical
Value
Sample Statistic
RejectionRegion
NonrejectionRegion
Rejection Region Rejection Region (one-tail (one-tail test)test)
Sampling DistributionSampling Distribution
1 -
Level of ConfidenceLevel of Confidence
![Page 13: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/13.jpg)
Levine, Prentice-Hall
HoValueCritical
Value
Sample Statistic
RejectionRegion
NonrejectionRegion
Rejection Region Rejection Region (one-tail (one-tail test)test)
Sampling DistributionSampling Distribution
1 -
Level of ConfidenceLevel of Confidence
Observed sample statisticObserved sample statistic
![Page 14: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/14.jpg)
Levine, Prentice-Hall
HoValueCritical
Value
Sample Statistic
RejectionRegion
NonrejectionRegion
Rejection Region Rejection Region (one-tail (one-tail test)test)
Sampling DistributionSampling Distribution
1 -
Level of ConfidenceLevel of Confidence
ObservedObserved sample statistic sample statistic
![Page 15: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/15.jpg)
Levine, Prentice-Hall
Rejection RegionsRejection Regions (two-(two-tailed test)tailed test)
HoValue Critical
ValueCriticalValue
1/2 1/2
Sample Statistic
RejectionRegion
RejectionRegion
NonrejectionRegion
Sampling Distribution
1 - 1 -
Level of Confidence
![Page 16: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/16.jpg)
Levine, Prentice-Hall
Rejection RegionsRejection Regions (two-(two-tailed test)tailed test)
HoValue Critical
ValueCriticalValue
1/2 1/2
Sample Statistic
RejectionRegion
RejectionRegion
NonrejectionRegion
Sampling Distribution
1 - 1 -
Level of Confidence
ObservedObserved sample statistic sample statistic
![Page 17: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/17.jpg)
Levine, Prentice-Hall
Rejection RegionsRejection Regions (two-(two-tailed test)tailed test)
HoValue Critical
ValueCriticalValue
1/2 1/2
Sample Statistic
RejectionRegion
RejectionRegion
NonrejectionRegion
Sampling Distribution
1 - 1 -
Level of Confidence
ObservedObserved sample statistic sample statistic
![Page 18: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/18.jpg)
Levine, Prentice-Hall
Rejection RegionsRejection Regions (two-(two-tailed test)tailed test)
HoValue Critical
ValueCriticalValue
1/2 1/2
Sample Statistic
RejectionRegion
RejectionRegion
NonrejectionRegion
Sampling Distribution
1 - 1 -
Level of Confidence
ObservedObserved sample statistic sample statistic
![Page 19: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/19.jpg)
Levine, Prentice-Hall
Risk of Errors in Making Risk of Errors in Making DecisionDecision
Type I errorType I error• Reject true null hypothesisReject true null hypothesis• Has serious consequencesHas serious consequences• Probability of Type I error is alpha [Probability of Type I error is alpha [
– Called level of significanceCalled level of significance Type II errorType II error
• Do not reject false null hypothesisDo not reject false null hypothesis• Probability of Type II error is beta [ Probability of Type II error is beta [
![Page 20: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/20.jpg)
Levine, Prentice-Hall
Decision ResultsDecision ResultsHH00: Innocent: InnocentJury Trial H0 Test
Actual Situation Actual Situation
Verdict Innocent Guilty Decision H0 True H0 False
Innocent Correct Error Do NotReject H0
CorrectType II
Error ()
Guilty Error Correct Reject H0Type I
Error ()Correct
![Page 21: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/21.jpg)
Levine, Prentice-Hall
Hypothesis TestingHypothesis Testing
State HState H00
State HState H11
Choose Choose
Choose Choose nn
Choose testChoose test
![Page 22: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/22.jpg)
Levine, Prentice-Hall
Hypothesis TestingHypothesis Testing
Set up critical valuesSet up critical values
Collect dataCollect data
Compute test statisticCompute test statistic
Make statistical decisionMake statistical decision
Express decisionExpress decision
State HState H00
State HState H11
Choose Choose
Choose Choose nn
Choose testChoose test
![Page 23: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/23.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
Does an average box of Does an average box of cereal contain 368 grams of cereal contain 368 grams of cereal? A random sample of cereal? A random sample of 25 boxes has an average 25 boxes has an average weight = 372.5 grams. The weight = 372.5 grams. The company has specified company has specified to to be 15 grams. Test at the .05 be 15 grams. Test at the .05 level.level.
368 gm.368 gm.
![Page 24: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/24.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
HH00: :
HH11: :
nn
Critical Value(s):Critical Value(s):
Test Statistic: Test Statistic:
Decision:Decision:
Conclusion:Conclusion:
![Page 25: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/25.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
HH00: : = 368 = 368
HH11: : 368 368
nn
Critical Value(s):Critical Value(s):
Test Statistic: Test Statistic:
Decision:Decision:
Conclusion:Conclusion:
![Page 26: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/26.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
HH00: : = 368 = 368
HH11: : 368 368
.05.05
nn 25 25
Critical Value(s):Critical Value(s):
Test Statistic: Test Statistic:
Decision:Decision:
Conclusion:Conclusion:
![Page 27: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/27.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
HH00: : = 368 = 368
HH11: : 368 368
.05.05
nn 25 25
Critical Value(s):Critical Value(s):
Test Statistic: Test Statistic:
Decision:Decision:
Conclusion:Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
![Page 28: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/28.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
HH00: : = 368 = 368
HH11: : 368 368
.05.05
nn 25 25
Critical Value(s):Critical Value(s):
Test Statistic: Test Statistic:
Decision:Decision:
Conclusion:Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
ZX
n
372 5 368
1525
150.
.
![Page 29: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/29.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
HH00: : = 368 = 368
HH11: : 368 368
.05.05
nn 25 25
Critical Value(s):Critical Value(s):
Test Statistic: Test Statistic:
Decision:Decision:
Conclusion:Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
ZX
n
372 5 368
1525
150.
.
Do not reject at = .05
![Page 30: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/30.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test
HH00: : = 368 = 368
HH11: : 368 368
.05.05
nn 25 25
Critical Value(s):Critical Value(s):
Test Statistic: Test Statistic:
Decision:Decision:
Conclusion:Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
ZX
n
372 5 368
1525
150.
.
Do not reject at = .05
No evidence No evidence average is not 368average is not 368
![Page 31: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/31.jpg)
Levine, Prentice-Hall
Z0 1.50-1.50
Two-tailed z-test Two-tailed z-test [p-value]][p-value]]
Z value of sample statistic
![Page 32: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/32.jpg)
Levine, Prentice-Hall
Z0 1.50-1.50
Two-tailed z-test Two-tailed z-test [p-value][p-value]
p-value is P(z -1.50 or z 1.50)
Z value of sample statistic
![Page 33: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/33.jpg)
Levine, Prentice-Hall
Z0 1.50-1.50
1/2 p-Value1/2 p-Value
Two-tailed z-test Two-tailed z-test [p-value][p-value]
p-value is P(z -1.50 or z 1.50)
Z value of sample statistic
![Page 34: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/34.jpg)
Levine, Prentice-Hall
Z0 1.50-1.50
1/2 p-Value1/2 p-Value
Two-tailed z-test Two-tailed z-test [p-value][p-value]
p-value is P(z -1.50 or z 1.50)
Z value of sample statistic
From Z table: lookup 1.50
.4332
![Page 35: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/35.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test [p-value][p-value]
Z0 1.50-1.50
1/2 p-Value.0668
1/2 p-Value.0668
p-value is P(z -1.50 or z 1.50)
Z value of sample statistic
From Z table: lookup 1.50
.4332
.5000- .4332
.0668
![Page 36: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/36.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test [p-value][p-value]
Z0 1.50-1.50
1/2 p-Value.0668
1/2 p-Value.0668
p-value is P(z -1.50 or z 1.50) = .1336
Z value of sample statistic
From Z table: lookup 1.50
.4332
.5000- .4332
.0668
![Page 37: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/37.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test [p-value][p-value]
0 1.50-1.50 Z
RejectReject
1/2 p-value = .06681/2 p-value = .0668
1/2 = .0251/2 = .025
![Page 38: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/38.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test [p-value][p-value]
0 1.50-1.50 Z
RejectReject
(p-Value = .1336) ( = .05)
Do not reject. 1/2 p-Value = .06681/2 p-Value = .0668
1/2 = .0251/2 = .025
Test statistic is in ‘Do not reject’ region
![Page 39: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/39.jpg)
Levine, Prentice-Hall
Two-tailed z-testTwo-tailed z-test (( known) known) challengechallenge
You are a Q/C inspector. You want to find You are a Q/C inspector. You want to find out if a new machine is making electrical out if a new machine is making electrical cords to customer specification: average cords to customer specification: average breaking strength of 70 lb. with breaking strength of 70 lb. with = 3.5 lb. = 3.5 lb. You take a sample of 36You take a sample of 36 cords & compute cords & compute a sample mean of 69.7a sample mean of 69.7 lb. At the .05lb. At the .05 level, is there evidence that the machine level, is there evidence that the machine is not meeting the average breaking is not meeting the average breaking strength?strength?
![Page 40: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/40.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test (( known)known)
HH00: :
HH11: :
= =
nn = =
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
![Page 41: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/41.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test (( known)known)
HH00: : = 70 = 70
HH11: : 70 70
= =
nn = =
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
![Page 42: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/42.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test (( known)known)
HH00: : = 70 = 70
HH11: : 70 70
= .05= .05
nn = 36 = 36
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
![Page 43: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/43.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test (( known)known)
HH00: : = 70 = 70
HH11: : 70 70
= .05= .05
nn = 36 = 36
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
![Page 44: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/44.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test (( known)known)
HH00: : = 70 = 70
HH11: : 70 70
= .05= .05
nn = 36 = 36
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
ZX
n
69 7 70
3 536
51.
..
![Page 45: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/45.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test (( known)known)
HH00: : = 70 = 70
HH11: : 70 70
= .05= .05
nn = 36 = 36
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
ZX
n
69 7 70
3 536
51.
..
Do not reject at = .05
![Page 46: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/46.jpg)
Levine, Prentice-Hall
Two-tailed z-test Two-tailed z-test (( known)known)
HH00: : = 70 = 70
HH11: : 70 70
= .05= .05
nn = 36 = 36
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.96-1.96
.025
Reject H 0 Reject H 0
.025
ZX
n
69 7 70
3 536
51.
..
Do not reject at = .05
No evidence average is not 70
![Page 47: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/47.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
AssumptionsAssumptions• Population is normally distributedPopulation is normally distributed• If not normal, can be approximated by If not normal, can be approximated by
normal distribution for large samplesnormal distribution for large samples
![Page 48: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/48.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
AssumptionsAssumptions• Population is normally distributedPopulation is normally distributed• If not normal, can be approximated by If not normal, can be approximated by
normal distribution for large samplesnormal distribution for large samples Null hypothesis has Null hypothesis has or or sign only sign only
![Page 49: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/49.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
AssumptionsAssumptions• Population is normally distributedPopulation is normally distributed• If not normal, can be approximated by If not normal, can be approximated by
normal distribution for large samplesnormal distribution for large samples Null hypothesis has Null hypothesis has or or sign only sign only Z-test statisticZ-test statistic
ZX X
n
x
x
![Page 50: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/50.jpg)
Levine, Prentice-Hall
Z0
Reject H 0
One-tailed z-test One-tailed z-test (( known) known)
H0:0 H1: < 0
Must be significantly below
![Page 51: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/51.jpg)
Levine, Prentice-Hall
Z0
Reject H 0
Z0
Reject H 0
One-tailed z-test One-tailed z-test (( known) known)
H0:0 H1: < 0
H0:0 H1: > 0
Must be significantly below
Small values satisfy H0 . Do not reject!
![Page 52: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/52.jpg)
Levine, Prentice-Hall
Z0
= 1
One-tailed z-test One-tailed z-test (( known) known)
What is “z” given = .025?
= .025
![Page 53: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/53.jpg)
Levine, Prentice-Hall
Z0
= 1
One-tailed z-test One-tailed z-test (( known) known)
.500 - .025
.475
What Is Z given = .025?
= .025
![Page 54: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/54.jpg)
Levine, Prentice-Hall
Z0
= 1 Z .05 .07
1.6 .4505 .4515 .4525
1.7 .4599 .4608 .4616
1.8 .4678 .4686 .4693
.4744 .4756
One-tailed z-test One-tailed z-test (( known) known)
.500 - .025
.475
.06
1.9 .4750
Standardized Normal Probability Table (Portion)
What is “z” given = .025?
= .025
![Page 55: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/55.jpg)
Levine, Prentice-Hall
Z0
= 1
1.96
Z .05 .07
1.6 .4505 .4515 .4525
1.7 .4599 .4608 .4616
1.8 .4678 .4686 .4693
.4744 .4756
One-tailed z-test One-tailed z-test (( known) known)
.500 - .025
.475
.06
1.9 .4750
Standardized Normal Probability Table (Portion)
What Is Z given = .025?
= .025
![Page 56: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/56.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known) known)
Does an average box of Does an average box of cereal contain more than cereal contain more than 368 grams of cereal? A 368 grams of cereal? A random sample of 25 random sample of 25 boxes showedboxes showedX = 372.5. X = 372.5. The company has The company has specified specified to be 15 grams. to be 15 grams. Test at the .05 level. Test at the .05 level. 368 gm.368 gm.
![Page 57: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/57.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
HH00: :
HH11: :
= =
n n = =
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
![Page 58: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/58.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
HH00: : 368 368
HH11: : > 368 > 368
= =
n n = =
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
![Page 59: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/59.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
HH00: : 368 368
HH11: : > 368 > 368
= .05= .05
n n = 25= 25
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
![Page 60: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/60.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
HH00: : 368 368
HH11: : > 368 > 368
= .05= .05
n n = 25= 25
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.645
.05
Reject
![Page 61: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/61.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
HH00: : 368 368
HH11: : > 368 > 368
= .05= .05
n n = 25= 25
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.645
.05
Reject
ZX
n
372 5 368
1525
150.
.
![Page 62: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/62.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
HH00: : 368 368
HH11: : > 368 > 368
= .05= .05
n n = 25= 25
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.645
.05
Reject
ZX
n
372 5 368
1525
150.
.
Do not reject at = .05
![Page 63: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/63.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test (( known)known)
HH00: : 368 368
HH11: : > 368 > 368
= .05= .05
n n = 25= 25
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Z0 1.645
.05
Reject
ZX
n
372 5 368
1525
150.
.
Do not reject at = .05
No evidence average is more than 368
![Page 64: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/64.jpg)
Levine, Prentice-Hall
Z0 1.50
One-tailed z-test One-tailed z-test ((
known)known) p-value Solutionp-value Solution
Z value of sample statistic
Use alternative hypothesis to find direction
![Page 65: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/65.jpg)
Levine, Prentice-Hall
Z0 1.50
p-Value.0668
One-tailed z-test One-tailed z-test ((
known)known) p-valuep-value
Z value of sample statistic
Use alternative hypothesis to find direction
![Page 66: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/66.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test ((
known)known) p-valuep-value
Z0 1.50
p-Value.0668
Z value of sample statistic
From Z table: lookup 1.50
..4332
Use alternative hypothesis to find direction
![Page 67: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/67.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test ((
known)known) p-valuep-value
Z0 1.50
p-Value.0668
Z value of sample statistic
From Z table: lookup 1.50
..4332
Use alternative hypothesis to find direction
.5000- .4332
.0668
![Page 68: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/68.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test ((
known)known) p-valuep-value
Z0 1.50
p-Value.0668
Z value of sample statistic
From Z table: lookup 1.50
..4332
Use alternative hypothesis to find direction
.5000- .4332
.0668
p-value = .0668
![Page 69: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/69.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test ((
known)known) p-valuep-value
0 1.50 Z
Reject
0 1.50 Z
Rejectp-value = .0668
= .05
![Page 70: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/70.jpg)
Levine, Prentice-Hall
One-tailed z-test One-tailed z-test ((
known)known) p-valuep-value
0 1.50 Z
Reject
0 1.50 Z
Reject
(p-value = .0668) ( = .05).
Do not reject.p-Value = .0668
= .05
Test statistic is in ‘Fail to reject’ region
![Page 71: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/71.jpg)
Levine, Prentice-Hall
p-valuep-value ChallengeChallenge
You’re an analyst for Ford. You want You’re an analyst for Ford. You want to find out if the average miles per to find out if the average miles per gallon of Escorts is at least 32 mpg. gallon of Escorts is at least 32 mpg. Similar models have a standard Similar models have a standard deviation of 3.8deviation of 3.8 mpg. You take a mpg. You take a sample of 60sample of 60 Escorts & compute a Escorts & compute a sample mean of 30.7sample mean of 30.7 mpg. What is mpg. What is the value of the observed level of the value of the observed level of significance (p-Value)?significance (p-Value)?
![Page 72: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/72.jpg)
Levine, Prentice-Hall
p-valuep-value
Z0-2.65
p-Value.004
Z value of sample statistic
From Z table: lookup 2.645
.4960.4960
Use alternative hypothesis to find direction
.5000- .4960
.0040
p-value = .004 p-value < ( = .01) Reject H0.
![Page 73: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/73.jpg)
Levine, Prentice-Hall
p-valuep-value
Probability of obtaining a test statistic more Probability of obtaining a test statistic more extreme (extreme (or or than actual sample than actual sample value given Hvalue given H00 is true is true
Called observed level of significanceCalled observed level of significance• Smallest value of Smallest value of H H00 can be rejected can be rejected
Used to make rejection decisionUsed to make rejection decision
• If p-value If p-value , reject H, reject H00
![Page 74: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/74.jpg)
Levine, Prentice-Hall
One-tailed t-test One-tailed t-test (( unknown)unknown)
Does an average box of Does an average box of cereal contain less than cereal contain less than the 368 grams indicated on the 368 grams indicated on the package? A random the package? A random sample of 25 boxes sample of 25 boxes showedshowedX = 363.5 and X = 363.5 and s=15. Test at the .05 level.s=15. Test at the .05 level.
368 gr.368 gr.
![Page 75: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/75.jpg)
Levine, Prentice-Hall
HH00: :
HH11: :
= =
n n = =
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
One-tailed t-test One-tailed t-test ((
unknown)unknown)
![Page 76: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/76.jpg)
Levine, Prentice-Hall
HH00: : 368 368
HH11: : < 368 < 368
= =
n n = =
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
One-tailed t-test One-tailed t-test ((
unknown)unknown)
![Page 77: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/77.jpg)
Levine, Prentice-Hall
HH00: : 368 368
HH11: : < 368 < 368
= .05= .05
n n = 25, d.f. = 24= 25, d.f. = 24
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
One-tailed t-test One-tailed t-test ((
unknown)unknown)
![Page 78: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/78.jpg)
Levine, Prentice-Hall
HH00: : 368 368
HH11: : < 368 < 368
= .05= .05
n n = 25, d.f. = 24= 25, d.f. = 24
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
One-tailed t-test One-tailed t-test ((
unknown)unknown)
![Page 79: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/79.jpg)
Levine, Prentice-Hall
HH00: : 368 368
HH11: : < 368 < 368
= .05= .05
n n = 25, d.f. = 24= 25, d.f. = 24
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
One-tailed t-test One-tailed t-test ((
unknown)unknown)
50.1
2515
3685 . 363
ns
Xt
![Page 80: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/80.jpg)
Levine, Prentice-Hall
HH00: : 368 368
HH11: : < 368 < 368
= .05= .05
n n = 25, d.f. = 24= 25, d.f. = 24
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
Do not reject at = .05
One-tailed t-test One-tailed t-test ((
unknown)unknown)
50.1
2515
3685 . 363
ns
Xt
![Page 81: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/81.jpg)
Levine, Prentice-Hall
HH00: : 368 368
HH11: : < 368 < 368
= .05= .05
n n = 25, d.f. = 24= 25, d.f. = 24
Critical Value(s):Critical Value(s):
Test Statistic:
Decision:
Conclusion:
50.1
2515
3685 . 363
ns
Xt
Do not reject at = .05
No evidence average is less than 368
One-tailed t-test One-tailed t-test ((
unknown)unknown)
![Page 82: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/82.jpg)
Levine, Prentice-Hall
One-tailed t-test One-tailed t-test ((
unknown)unknown) p-value Solutionp-value Solution
t value of sample statistic
Use alternative hypothesis to find direction
![Page 83: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/83.jpg)
Levine, Prentice-Hall
One-tailed t-test One-tailed t-test ((
unknown)unknown) p-valuep-value
Use alternative hypothesis to find direction
t value of sample statistic
From t table: lookup -1.50 for 24 d.f.
P-value P-value = 0.075= 0.075
![Page 84: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/84.jpg)
Levine, Prentice-Hall
p-value = .075
= .05
One-tailed t-test One-tailed t-test ((
unknown)unknown) p-valuep-value
![Page 85: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/85.jpg)
Levine, Prentice-Hall
p-value = .075
= .05
One-tailed t-test One-tailed t-test ((
unknown)unknown) p-valuep-value
Test statistic is in ‘Fail to reject’ region
(p-value = .075) ( = .05).
Do not reject.
Reject
![Page 86: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/86.jpg)
Questions?Questions?
![Page 87: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/87.jpg)
ANOVAANOVA
![Page 88: Hypothesis Testing Variance known?. Sampling Distribution n Over-the-counter stock selling prices calculate average price of all stocks listed [ ]calculate](https://reader035.vdocuments.us/reader035/viewer/2022062621/551c0a87550346ad4f8b50a7/html5/thumbnails/88.jpg)