Unfortunately for us these snow days ultimately just mean less time for us to learn everything for the AP Exam (May 11th)! Therefore I need you all to step your game up and put in some strong effort for your homework--teaching yourself chapter 21!
For homework tonight/tomorrow please be sure to complete the chapter 21 reading questions and vocab quiz provided in class (or below)!
- Get this done! No excuses!
- It is essential you put in max effort to learn about chapter 21 on your own! We'll be having a test that includes this content soon!
- Chapter 21 Reading Questions:
- Use your textbook to answer each of the questions below. We only have 1 to 2 days to review this stuff, so you have to teach yourself the foundational terms/concepts yourself—via these questions! Record the answers in your notebook (these are your notes!)
- What is a p-value? Record the definition of p-value—highlighted in blue on page 476.
- Below this blue section there is a sentence in italics about what the p-value is NOT (on p. 476). Copy this sentence below!
- Record the highlighted blue text on the top half of page 477.
- Now, read the bottom of page 477, “Alpha Levels.” This references alpha levels and statistical significance; record the blue statement on the bottom of p. 477, and the blue section on the top of p. 478 in your own words.
- Much of this chapter delves deeper into the details about hypothesis testing. However, we are going to introduce two new ideas: type I and type II error!
- What is a type one error? (read the bottom of p. 482)
- What is/define a type two error.
- An alpha level represents the “cutoff” value we use to decide if we reject the null hypothesis—but it’s also connected to Type I error. How so? Look at one of the blue highlighted pieces on page 483 and state how alpha relates to Type I error.
- What is the power of a test? (blue stuff on page 483 AND on read the “power” section on p. 484).
- Read the entire section about power on p. 484 and record your own notes about power!
- How do we calculate power? (look at the bullets on p. 487)
- What is effect size? (p. 485)
Chapter 21: Types of Error
- In attempt to increase the percentage of people wearing seat belts, Massachusetts instituted a “click-it or ticket” policy. Use of safety belts rose to 62% in 2003, with a goal of surpassing 80% by 2005. That year (in 2005), of 134 stopped drivers, 23 were not wearing their seatbelt. Does this provide evidence of meeting the goal? If we have met the goal, Massachusetts will cut back funding on the “click-it or ticket” program.
- Define each type of error and a consequence of each.
- If we use an alpha level of 0.05, what is the associated confidence level?
- A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company’s product. The radio station conducts a random phone survey of 400 people.
- Write the hypotheses.
- Define a Type I error and identify a potential consequence.
- Define a Type 2 error and identify a potential consequence.
- Which alpha level--.01, .05, or .10—will maximize the power of this test?
- The company proposes the station call 600 people rather than 400. How will this affect the power? Will this make the risk of a Type I/Type II higher or lower?
- Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. Recently, a group of researchers devised a 7 minute test to serve as a quick screen for the disease for use in the general population of senior citizens. A patient who tested positive would then go through the more expensive battery of tests and medical diagnosis. The authors reported a false positive rate of 4% and a false negative rate of 8%.
- Define a Type I error and identify a potential consequence.
- Define a Type 2 error and identify a potential consequence.
- What is the alpha level?
- Calculate the power of this test.
UPCOMING TEST INFO:
- We have a test coming up that covers all of chapters 19-21: confidence intervals and hypothesis tests!
- Our test will either be on Thursday (3/16) or Monday (3/20)--we'll have to see what happens with all this snow!
- Either way, start preparing now!
- Here are some chapter 19-21 summary/review questions you can use if you'd like to start preparing:
- AP Statistics Test Review: Ch. 19,20, 21 (hw for night before test)Mr. Carofano plans to estimate the true percentage of EHHS underclassmen who plan to take AP Statistics. He takes a sample of 120 underclassmen, and 29 of them plan to take AP Statistics. Based on past data, it is believe that approximately 10% of underclassmen take AP Statistics.
- Verify that the conditions for inference are satisfied.
- Calculate the margin of error for this sample (98% confidence).
- Estimate the true percentage of underclassmen who plan to take AP Stat using a 98% confidence interval.
- Interpret the meaning of this interval.
- Explain the meaning of “98% confidence.”
- How can Mr. Carofano narrow the width of his interval? What would cause the interval to widen?
- Based on your interval, do you believe the percentage of underclassmen who plan to take AP Stat has risen?
- Is there significant evidence to suggest that the percentage of underclassmen taking AP Stat is rising? Conduct and appropriate test at the 5% level of significance. (hypotheses, conditions, math, conclusion).
- Explain the meaning of the p-value, in context.
- If the percentage of students in AP Statistics has risen, more sections of the course will be offered and another teacher will be hired. If not, there will only be 3 classes offered.
- Identify the meaning of a Type I and Type II error in context.
- Identify a consequence of each.
- The probability of a Type I error is 5%, and the probability of a Type II is 15%. Calculate the power.
- Explain the meaning of the power of this test, in context.
- If Mr. Carofano wants a margin of error of only 4%, what sample size should be used (at 98% confidence)?
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