《商务统计学概论》（英文版） CHAPTER 10: Hypothesis Testing, One Population Mean or Proportion

CHAPTER 10 Hypothesis Testing, One population Mean or proportion to accompany Introduction to business statistics fourth edition by ronald M. Weiers Presentation by priscilla Chaffe-Stengel Donald n. Stengel o 2002 The Wadsworth Group

CHAPTER 10: Hypothesis Testing, One Population Mean or Proportion to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group

l Chapter 10- Learning objectives Describe the logic of and transform verbal statements into null and alternative hypotheses Describe what is meant by Type I and Type II errors Conduct a hypothesis test for a single population mean or proportion Determine and explain the p-value of a test statistic Explain the relationship between confidence intervals and hypothesis tests o 2002 The Wadsworth Group

Chapter 10 - Learning Objectives • Describe the logic of and transform verbal statements into null and alternative hypotheses. • Describe what is meant by Type I and Type II errors. • Conduct a hypothesis test for a single population mean or proportion. • Determine and explain the p-value of a test statistic. • Explain the relationship between confidence intervals and hypothesis tests. © 2002 The Wadsworth Group

I Null and alternative hypotheses Null hypotheses Ho: Put here what is typical of the populatio a term that at characterizes business as usua/e where nothing out of the ordinary occurs Alternative Hypotheses H: Put here what is the challenge, the view of some characteristic of the population that, if it were true, would trigger some new action, some change in procedures that had previously defined business as usual o 2002 The Wadsworth Group

Null and Alternative Hypotheses • Null Hypotheses – H0 : Put here what is typical of the population, a term that characterizes “business as usual” where nothing out of the ordinary occurs. • Alternative Hypotheses – H1 : Put here what is the challenge, the view of some characteristic of the population that, if it were true, would trigger some new action, some change in procedures that had previously defined “business as usual.” © 2002 The Wadsworth Group

l Beginning an example When a robot welder is in adjustment, its mean time to perform its task is 1.3250 minutes. past experience has found the standard deviation of the cycle time to be 0. 0396 minutes. An incorrect mean operating time can disrupt the efficiency of other activities along the production line. For a recent random sample of 80 jobs the mean cycle time for the welder was 1.3229 minutes Does the machine appear to be in need of adjustment? o 2002 The Wadsworth Group

Beginning an Example • When a robot welder is in adjustment, its mean time to perform its task is 1.3250 minutes. Past experience has found the standard deviation of the cycle time to be 0.0396 minutes. An incorrect mean operating time can disrupt the efficiency of other activities along the production line. For a recent random sample of 80 jobs, the mean cycle time for the welder was 1.3229 minutes. Does the machine appear to be in need of adjustment? © 2002 The Wadsworth Group

l Building Hypotheses What decision is to be made? The robot welder is in adjustment The robot welder is not in adjustment How will we decide? In adjustment means u=1. 3250 minutes Not in adjustment means u* 1. 3250 minutes Which requires a change from business as usual? What triggers new action Not in adjustment-H1:μ≠1.3250 minutes o 2002 The Wadsworth Group

Building Hypotheses • What decision is to be made? – The robot welder is in adjustment. – The robot welder is not in adjustment. • How will we decide? – “In adjustment” means µ = 1.3250 minutes. – “Not in adjustment” means µ  1.3250 minutes. • Which requires a change from business as usual? What triggers new action? – Not in adjustment - H1 : µ  1.3250 minutes © 2002 The Wadsworth Group

Ⅷ Types of error State of realit Ho True Ho False ype Test True 0 No error error Says TYp e l error No error False o 2002 The Wadsworth Group

Types of Error No error Type II error: b Type I error: a No error State of Reality H0 True H0 False H0 True H0 False Test Says © 2002 The Wadsworth Group

l Types of error ype I error Saying you reject Ho when it really is true Rejecting a true Ho ° Type I error: saying you do not reject ho when it really is false Failing to reject a false h o 2002 The Wadsworth Group

Types of Error • Type I Error: – Saying you reject H0 when it really is true. – Rejecting a true H0 . • Type II Error: – Saying you do not reject H0 when it really is false. – Failing to reject a false H0 . © 2002 The Wadsworth Group

I Acceptable Error for the example Decision makers frequently use a 570 significance level -Usea=0.05 An a-error means that we will decide to adjust the machine when it does not need adjustment This means, in the case of the robot welder if the machine is running properly, there is only a 0.05 probability of our making the mistake of concluding that the robot requires adjustment when it really does not o 2002 The Wadsworth Group

Acceptable Error for the Example • Decision makers frequently use a 5% significance level. – Use a = 0.05. – An a-error means that we will decide to adjust the machine when it does not need adjustment. – This means, in the case of the robot welder, if the machine is running properly, there is only a 0.05 probability of our making the mistake of concluding that the robot requires adjustment when it really does not. © 2002 The Wadsworth Group

l The Null Hypothesis Nondirectional, two-tail test Ho: pop parameter = value Directional, right-tail test 0: pop parameter< value Directional, left -tail test. pop parameter z value Always put hypotheses in terms of population parameters. Ho always gets o 2002 The Wadsworth Group

The Null Hypothesis • Nondirectional, two-tail test: – H0 : pop parameter = value • Directional, right-tail test: – H0 : pop parameter  value • Directional, left-tail test: – H0 : pop parameter  value Always put hypotheses in terms of population parameters. H0 always gets “=“. © 2002 The Wadsworth Group

I Nondirectional, Two-Tail tests Ho pop parameter=value H1: pop parameter value Do Not Reject H Reject H Reject H 0 0 2 杬 Z o 2002 The Wadsworth Group

Nondirectional, Two-Tail Tests H0 : pop parameter = value H1 : pop parameter  value a −a a 杬 +z Do Not Reject H 0 Reject H 0 Reject H 0 © 2002 The Wadsworth Group