Thursday HW = Important Test Review (ch. 21)

**Period E and F Students**

• If you will be out tomorrow for the honors assembly please stop by at some point tomorrow (before school, after school, or during B,G, or H period) to get our stamp problem and the key for tonight's homework
• Tonight's homework and tomorrow's stamp are direct review for Monday's test!
• If you are free period A feel free to come to our period A Stat class so you don't miss anything!

Tonight please complete the "Types of Error" practice worksheet provided in class (or below)! These questions summarize what we need to know about types of error and power and is some essential practice for our test!

Chapter 21: Types of Error

1. 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.
   1. Define each type of error and a consequence of each.
   2. If we use an alpha level of 0.05, what is the associated confidence level? (consider this: we have a one tailed test; if we're considering a 5% alpha level, that means we're trying to "cut off" 5% on the right side (since the Ha is >); the confidence interval/level is between these two regions cut off by the alpha level. If we cut off 5% on the right, we must do the same on the left (symmetric curve); what % does that leave for the middle? That's our C. Level)
                 
2. 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.
   1. Write the hypotheses.
   2. Define a Type I error and identify a potential consequence.
   3. Define a Type 2 error and identify a potential consequence.
   4. Which alpha level--.01, .05, or .10—will maximize the power of this test?
   5. 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?
3. 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%.
   1. Define a Type I error and identify a potential consequence.
   2. Define a Type 2 error and identify a potential consequence.
   3. What is the alpha level?
   4. Calculate the power of this test.

Ch. 19 - 21 TEST MONDAY!

• We have a test coming up that covers all of chapters 19-21: confidence intervals and hypothesis tests!
•  Start preparing now!
• Here are some chapter 19-21 summary/review questions you can use if you'd like to start preparing:

1. 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.
   1. Verify that the conditions for inference are satisfied.
   2. Calculate the margin of error for this sample (98% confidence).
   3. Estimate the true percentage of underclassmen who plan to take AP Stat using a 98% confidence interval.
   4. Interpret the meaning of this interval.
   5. Explain the meaning of “98% confidence.”
   6. How can Mr. Carofano narrow the width of his interval? What would cause the interval to widen?
   7. Based on your interval, do you believe the percentage of underclassmen who plan to take AP Stat has risen?
   8. 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).
   9. Explain the meaning of the p-value, in context.
   10. 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.
       1. Identify the meaning of a Type I and Type II error in context.
       2. Identify a consequence of each.
   11. The probability of a Type I error is 5%, and the probability of a Type II is 15%. Calculate the power.
   12. Explain the meaning of the power of this test, in context.
   13. If Mr. Carofano wants a margin of error of only 4%, what sample size should be used (at 98% confidence)?