AP StatisticsTuesday, 25 February 2014 • OBJECTIVETSW identify Type I and Type II Errors in hypothesis testing. • Friday, 28 February 2014 • Do not come to my room; instead, go to the computer lab in the (back of the) library. • REMINDER • PI Day will be celebrated Friday, 14 March 2014. • If you bring a pie, you may leave it in my room before 1st period. • Unless you can keep something cold on your own, do NOT bring anything that needs to be refrigerated!
Calendars are not yet ready • Tuesday, 25 February 2014 • Read: pp. 526-530 • Do: 10.11, 10.15, and 10.18 • Due Friday, 28 February 2014. • PowerPoint: Type I and Type II Errors • WS Errors WS #1 • Due by end of period Thursday, 27 February 2014. • Thursday, 27 February 2014 • Finish PowerPoint: Type I and Type II Errors • PowerPoint: Power of a Test • WS Errors WS #2 • Due on Friday, 28 February 2014. • Friday, 27 February • Read: pp. 556-564 − QUIZ: Type I and Type II Errors • Do: 10.61, 10.63, 10.64 ∙ On Monday, 03 March 2014. • Due on Monday, 03 March 2014. • Internet Activity: Power of a Significance Test • WS Power of a Significance Test • Due on Monday, 03 March 2014.
When you perform a hypothesis test you make a decision: reject H0or fail to reject H0 When you make one of these decisions, there is a possibility that you could be wrong! That you made an error!
There are two decisions that we make; reject or fail to reject. Each could possibly be a wrong decision; therefore, there are two types of errors.
a m0 Type I error • When you reject the null hypothesis that is really true • Denoted by a • Is the level of significance of the test
Fail to reject Reject Type II error • When you fail to reject the null hypothesis when it is false • Denoted by b Type I – reject a true H0 The x-bar is really part of the H0 curve, but we mistake it as being part of the Ha curve The x-bar is really part of the Ha curve, but we mistake it as being part of the H0 curve a Type II – fail to reject a false H0 b
Type I error Correct a Suppose H0 is false & we reject it, what type of decision was made? Type II error Correct Suppose H0 is false & we fail to reject it, what type of decision was made? Suppose H0 is true & we reject it, what type of decision was made? Suppose H0 is true & we fail to reject it, what type of decision was made? b
How do we word statements of type I & type II errors? “We say this decision when in reality this is true.” You replace the red, underlined words with words from context!
Consequences – are NOT the definitions of type I & II errors. They are what happens as a resultof making that incorrect decision.
What are the hypotheses? Type I error – Consequence: Type II error – Consequence: Consider a murder trial: Type I - that is why there must be evidence beyond a reasonable doubt! We don’t want to send innocent people to jail! H0: defendant is innocent Ha: defendant is guilty Say the defendant is guilty when really innocent An innocent person goes to prison Which of these errors does our society believe to be worse? Say defendant is not guilty when really guilty A guilty person goes free
Facts: As a increases, b decreases As a decreases, b increases • Every time you make a decision, you have potentially made an error. • a & b are inversely related Fail to reject H0 Reject H0 a m0 b ma
Facts continued: • The seriousness of the error types is determined by the specific situations. • Depending upon the situation type I or type II may be the more serious. • We often DO NOT know if an error is made in real life. • Except for cases like • Firestone tires • Drugs like: Phen-phen & Vioxx Someone made an error with these products
AP StatisticsThursday, 27 February 2014 • OBJECTIVETSW identify Type I and Type II Errors in hypothesis testing. • ASSIGNMENT DUE TODAY • WS Error WS #1 wire basket • ASSIGNMENTS DUE TOMORROW • WS Error Types #2 • Bookwork: 10.11, 10.15, 10.18 • Tomorrow, Friday, 28 February 2014: Go to computer lab in back of library. • REMINDER:PI Day celebration on Friday, 03/14/14.
Example 1: Lay’s Chip Company decides to accept a truckload of potatoes based upon results from a sample of potatoes from the truckload. What are the hypotheses? Type I error? Type II error? From the supplier’s viewpoint, which is more serious? From the chip company’s viewpoint, which is more serious? H0: potatoes good Ha: potatoes bad Say the potatoes are bad when they really are good Say the potatoes are good when they really are bad Sometimes, the seriousness depends upon the person’s point-of-view A type I error A type II error
Example 2:Water samples are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150oF, there will be no negative effects on the river’s ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge above 150oF, fifty water samples will be taken at randomly selected times, and the temperature of each sample recorded. What are the hypotheses? What are the Type I and II errors? Which is more serious? H0: m = 150 Ha: m >150 Type I : Say the temperature is above 150° when it’s really not. Most people would agree that the type II error would be more serious because it would endanger the river’s ecosystem. Type II: Say the temperature isn’t above 150° when it’s really above. where μ is the true mean water temperature (oF)
Example 3: A doctor is considering a new medication to help fight infections. However, the medication has the possibility of being highly toxic to the patient. You will test the medication to determine toxicity. What are the hypotheses? What are the Type I & II errors? Which is more serious? H0: medicine is not toxic Ha: medicine is toxic Type I: say medicine is toxic when it really isn’t Type II : say medicine isn’t toxic when it really is Most would consider a type II error more serious since people could be harmed.
How does one decide what a level to use? After assessing the consequences of type I and type II errors, identify the largest a that is tolerable for the problem. Use that a level for your level of significance.
Assignment • WS Error WS #1 • Due by the end of the period today (wire basket). • WS Error WS #2 • Due tomorrow, Friday, 28 February 2014. • I will give the next 30 minutes to finish, then I will show the next PowerPoint: Power of a Significance Test.