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การทดสอบสมมติฐานทางสถิติ (Hypothesis Testing) ผู้ช่วยศาสตราจารย์วิศิษฐ์ ลิ้มสมบุญชัย ภาควิชาเศรษฐศาสตร์เกษตรและทรัพยากร คณะเศรษฐศาสตร์  มหาวิทยาลัยเกษตรศาสตร์
สมมติฐาน  (Hypothesis) ,[object Object]
การทดสอบสมมติฐาน  (Hypothesis testing) ,[object Object],[object Object],[object Object]
ขั้นตอนการทดสอบสมมติฐาน ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
ขั้นตอนการทดสอบสมมติฐาน  (1) ,[object Object],[object Object],[object Object],H 0 :    H 0 :    H 0 :  H 1 :    H 1 :    H 1 :
ขั้นตอนการทดสอบสมมติฐาน  (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],
Type I and Type II Error   Population Condition   Conclusion       H 0  True   H a  True Accept   H 0   Correct   Type II     Conclusion  Error Reject   H 0   Type I   Correct   Error   Conclusion
ขั้นตอนการทดสอบสมมติฐาน  (3) ,[object Object],[object Object],[object Object]
การทดสอบค่าเฉลี่ยประชากรชุดเดียว ,[object Object],[object Object]
การทดสอบค่าเฉลี่ยประชากรชุดเดียว  (1) n  >  30 ?    known ? Popul.  approx. normal  ?    known ? Use  s  to estimate   Use  s  to estimate   Increase  n to  >  30 Yes Yes Yes Yes No No No No
Example:  Metro EMS A major west coast city provides one of the most comprehensive emergency medical services in the world.  Operating in a multiple hospital system with approximately 20 mobile medical units, the service goal is to respond to medical emergencies with a mean time of 12 minutes or less. The director of medical services wants to formulate a hypothesis test that could use a sample of emergency response times to determine whether or not the service goal of 12 minutes or less is being achieved.
Example:  Metro EMS Let  n = 40,  = 13.25 minutes, S = 3.2 minutes ,[object Object],[object Object],[object Object],[object Object],[object Object],1.645
Example: Glow Toothpaste   The production line for Glow toothpaste is designed to fill tubes of toothpaste with a mean weight of 6 ounces.  Periodically, a sample of 30 tubes will be selected in order to check the filling process.  Quality assurance procedures call for the continuation of the filling process if the sample results are consistent with the assumption that the mean filling weight for the population of toothpaste tubes is 6 ounces; otherwise the filling process will be stopped and adjusted.
Example: Glow Toothpaste Let  n = 30,  = 6.1 ounces,  S = 0.2 ounces ,[object Object],[object Object],[object Object],[object Object],[object Object],1.96 - 1.96
Example: Glow Toothpaste Using p-value or prob. Value. 1.96 2.74 Prob. = 0.0031 ,[object Object],[object Object],[object Object]
การทดสอบค่าสัดส่วน  (Proportion) ,[object Object],[object Object],[object Object],[object Object]
Example: NSC For a Christmas and New Year’s week, the National Safety Council estimated that 500 people would be killed and 25,000 injured on the nation’s roads.  The NSC claimed that 50% of the accidents would be caused by drunk driving. A sample of 120 accidents showed that 67 were caused by drunk driving.  Use these data to test the NSC’s claim with
Example: NSC ,[object Object],[object Object],[object Object],[object Object],[object Object],1.96 - 1.96
Example: NSC Using p-value or prob. Value. 1.28 Prob. = 0.1006 ,[object Object],[object Object],[object Object]
การทดสอบค่าเฉลี่ยกรณีประชากร  2  ชุด  ( การทดสอบผลต่างค่าเฉลี่ย ) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
การทดสอบผลต่างค่าเฉลี่ย  (1) ,[object Object],[object Object]
การทดสอบผลต่างค่าเฉลี่ย  (2) ,[object Object],[object Object]
การทดสอบผลต่างค่าเฉลี่ย  (3) ,[object Object],[object Object]
Example: Par, Inc.   Par, Inc. is a manufacturer of golf equipment and has developed a new golf ball that has been designed to provide “extra distance.”  In a test of driving distance using a mechanical driving device, a sample of Par golf balls was compared with a sample of golf balls made by Rap, Ltd., a competitor.  The sample statistics appear on the next slide.
Example: Par, Inc. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example: Par, Inc. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example: Specific Motor Specific Motors of Detroit has developed a new automobile known as the M car.  12 M cars and 8 J cars (from Japan) were road tested to compare miles-per-gallon (mpg) performance. The sample statistics are: Sample #1    Sample #2   M Cars   J Cars Sample Size n 1  = 12 cars   n 2  = 8 cars Mean   = 29.8 mpg  = 27.3 mpg Standard Deviation  s 1  = 2.56 mpg   s 2  = 1.81 mpg
Example: Special Motor ,[object Object],[object Object],[object Object],[object Object],[object Object]
การทดสอบค่าสัดส่วนกรณีประชากร  2  ชุด  ( การทดสอบผลต่างค่าสัดส่วน ) โดยที่  คือ  Sample proportion
Example: MRA. Market Research Associates (MRA.) is conducting research to evaluate the effectiveness of a client’s new advertising campaign.  Before the new campaign began, a telephone survey of 150 households in the test market area showed 60 households “aware” of the client’s product.  The new campaign has been initiated with TV and newspaper advertisements running for three weeks.  A survey conducted immediately after the new campaign showed 120 of 250 households “aware” of the client’s product. Does the data support the position that the advertising campaign has provided an increased awareness of the client’s product?
Example: MRA. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Note:  Point Estimator of  where P 1  = P 2 โดยที่

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สมมติฐานทางสถิติ

  • 1. การทดสอบสมมติฐานทางสถิติ (Hypothesis Testing) ผู้ช่วยศาสตราจารย์วิศิษฐ์ ลิ้มสมบุญชัย ภาควิชาเศรษฐศาสตร์เกษตรและทรัพยากร คณะเศรษฐศาสตร์ มหาวิทยาลัยเกษตรศาสตร์
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7. Type I and Type II Error Population Condition Conclusion H 0 True H a True Accept H 0 Correct Type II Conclusion Error Reject H 0 Type I Correct Error Conclusion
  • 8.
  • 9.
  • 10. การทดสอบค่าเฉลี่ยประชากรชุดเดียว (1) n > 30 ?  known ? Popul. approx. normal ?  known ? Use s to estimate  Use s to estimate  Increase n to > 30 Yes Yes Yes Yes No No No No
  • 11. Example: Metro EMS A major west coast city provides one of the most comprehensive emergency medical services in the world. Operating in a multiple hospital system with approximately 20 mobile medical units, the service goal is to respond to medical emergencies with a mean time of 12 minutes or less. The director of medical services wants to formulate a hypothesis test that could use a sample of emergency response times to determine whether or not the service goal of 12 minutes or less is being achieved.
  • 12.
  • 13. Example: Glow Toothpaste The production line for Glow toothpaste is designed to fill tubes of toothpaste with a mean weight of 6 ounces. Periodically, a sample of 30 tubes will be selected in order to check the filling process. Quality assurance procedures call for the continuation of the filling process if the sample results are consistent with the assumption that the mean filling weight for the population of toothpaste tubes is 6 ounces; otherwise the filling process will be stopped and adjusted.
  • 14.
  • 15.
  • 16.
  • 17. Example: NSC For a Christmas and New Year’s week, the National Safety Council estimated that 500 people would be killed and 25,000 injured on the nation’s roads. The NSC claimed that 50% of the accidents would be caused by drunk driving. A sample of 120 accidents showed that 67 were caused by drunk driving. Use these data to test the NSC’s claim with
  • 18.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 24. Example: Par, Inc. Par, Inc. is a manufacturer of golf equipment and has developed a new golf ball that has been designed to provide “extra distance.” In a test of driving distance using a mechanical driving device, a sample of Par golf balls was compared with a sample of golf balls made by Rap, Ltd., a competitor. The sample statistics appear on the next slide.
  • 25.
  • 26.
  • 27. Example: Specific Motor Specific Motors of Detroit has developed a new automobile known as the M car. 12 M cars and 8 J cars (from Japan) were road tested to compare miles-per-gallon (mpg) performance. The sample statistics are: Sample #1 Sample #2 M Cars J Cars Sample Size n 1 = 12 cars n 2 = 8 cars Mean = 29.8 mpg = 27.3 mpg Standard Deviation s 1 = 2.56 mpg s 2 = 1.81 mpg
  • 28.
  • 29. การทดสอบค่าสัดส่วนกรณีประชากร 2 ชุด ( การทดสอบผลต่างค่าสัดส่วน ) โดยที่ คือ Sample proportion
  • 30. Example: MRA. Market Research Associates (MRA.) is conducting research to evaluate the effectiveness of a client’s new advertising campaign. Before the new campaign began, a telephone survey of 150 households in the test market area showed 60 households “aware” of the client’s product. The new campaign has been initiated with TV and newspaper advertisements running for three weeks. A survey conducted immediately after the new campaign showed 120 of 250 households “aware” of the client’s product. Does the data support the position that the advertising campaign has provided an increased awareness of the client’s product?
  • 31.
  • 32. Note: Point Estimator of where P 1 = P 2 โดยที่