Lesson05_new

Statistics for Management Lesson 5 Fundamentals of Hypothesis Testing

Lesson Topics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],The Null Hypothesis, H 0 ,[object Object],[object Object]

[object Object],[object Object],[object Object],The Alternative Hypothesis, H 1

[object Object],[object Object],[object Object],[object Object],[object Object],Identify the Problem

Population Assume the population mean age is 50. (Null Hypothesis) REJECT The Sample Mean Is 20 Sample Null Hypothesis Hypothesis Testing Process No, not likely!

Sample Mean  = 50 Sampling Distribution 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 null hypothesis that  = 50. 20 H 0 Reason for Rejecting H 0

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Level of Significance, 

Level of Significance,  and the Rejection Region H 0 :   3 H 1 :  < 3 0 0 0 H 0 :   3 H 1 :  > 3 H 0 :   3 H 1 :   3    /2 Critical Value(s) Rejection Regions

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Errors in Making Decisions

H 0 : Innocent Jury Trial Hypothesis Test Actual Situation Actual Situation Verdict Innocent Guilty Decision H 0 True H 0 False Innocent Correct Error Do Not Reject H 0 1 -  Type II Error (  ) Guilty Error Correct Reject H 0 Type I Error (  ) Power (1 -  ) Result Possibilities

  Reduce probability of one error and the other one goes up.  &   Have an Inverse Relationship

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Factors Affecting Type II Error,       n

[object Object],[object Object],[object Object],[object Object],[object Object],2. Hypothesis Testing: Steps Test the Assumption that the true mean # of TV sets in US homes is at least 3.

[object Object],[object Object],[object Object],[object Object],[object Object],Hypothesis Testing: Steps Test the Assumption that the average # of TV sets in US homes is at least 3. (continued)

[object Object],[object Object],[object Object],3. Z-Test Statistics (  Known) Test Statistic X

[object Object],[object Object],[object Object],[object Object],[object Object],One-Tail Z Test for Mean (  Known)

Z 0  Reject H 0 Z 0 Reject H 0  H 0 :  H 1 :  < 0 H 0 :  0 H 1 :  > 0 Must Be Significantly Below  = 0 Small values don’t contradict H 0 Don’t Reject H 0 ! Rejection Region

[object Object],368 gm. Example: One Tail Test H 0 :  368 H 1 :  > 368 _

Z .04 .06 1.6 . 5495 . 5505 .5515 1.7 .5591 .5599 .5608 1.8 .5671 .5678 .5686 .5738 .5750 Z 0  Z = 1 1.645 .50 -. 05 .45 . 05 1.9 .5744 Standardized Normal Probability Table (Portion) What Is Z Given   = 0.05 ?  = .05 Finding Critical Values: One Tail Critical Value = 1.645

[object Object],[object Object],[object Object],Test Statistic: Decision: Conclusion: Do Not Reject at  = .05 No Evidence True Mean Is More than 368 Z 0 1.645 .05 Reject Example Solution: One Tail H 0 :  368 H 1 :  > 368

[object Object],368 gm. Example: Two Tail Test H 0 :  368 H 1 :  368

[object Object],[object Object],[object Object],Test Statistic: Decision: Conclusion: Do Not Reject at  = .05 No Evidence that True Mean Is Not 368 Z 0 1.96 .025 Reject Example Solution: Two Tail -1.96 .025 H 0 :  386 H 1 :  386

Connection to Confidence Intervals ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],_

[object Object],[object Object],[object Object],[object Object],[object Object],t-Test:  Unknown

Example: One Tail t-Test Does an average box of cereal contain more than 368 grams of cereal? A random sample of 36 boxes showed X = 372.5 , and  S= 15 . Test at the  0.01 level. 368 gm. H 0 :   368 H 1 :  368  is not given,

[object Object],[object Object],[object Object],Test Statistic: Decision: Conclusion: Do Not Reject at  = .01 No Evidence that True Mean Is More than 368 Z 0 2.4377 .01 Reject Example Solution: One Tail H 0 :  368 H 1 :  368

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],4. Proportions

Example:Z Test for Proportion ,[object Object],[object Object],[object Object]

[object Object],[object Object],Do not reject at  = .05 Z Test for Proportion: Solution H 0 : p  .04 H 1 : p  .04 Critical Values:  1.96 Test Statistic: Decision: Conclusion: We do not have sufficient evidence to reject the company’s claim of 4% response rate. Z  p - p p (1 - p) n s = .04 -.05 .04 (1 - .04) 500 = -1.14 Z 0 Reject Reject .025 .025

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