"Were it not for number and its nature, nothing that exists would be clear to anybody either in itself or in its relation to other things. You can observe the power of number exercising itself in all the acts and the thoughts of men."- (Philolaus, a Pythagorean, 5th century B.C.) Grace Chisholm Young (1864-1944): The English-born Young was one of the first to demonstrate applications of set theory to problems in mathematical analysis. She overcame considerable prejudice against women to achieve a Ph.D. in mathematics from Gottingen University in Germany in 1895. Her most distinguished work appears in a group of papers published from 1914 to 1916 in which she presented and developed theories and concepts in differential calculus. Young was a well-loved, generous woman with a variety of talents and tremendous energy. Why did Herkimer raise his son to be nasty in a very quiet way? Answer: He was told that children should be obscene, but not heard. Herky wants to know: What should you assume when a sign on a tailor shop reads "Closed for alterations?" When you read an autobiography, why do you learn nothing about the history of cars? ASSIGNMENT #63 Reading: Section 10.2, pages 550-556. (Understand SUMMARY on page 556) Exercises: 10.41, 10.43 (page 553), 10.44 (page 555). Write these up just as you would on the AP Exam.

You are working in Section 10.2.

When you choose a levelof significance , you are really settingthe probability that a Type I Error will be made. If the level ofsignificance is 5%, then you can expect to reject a correct nullhypothesis about 5% of the time. While we are not really studyingerror types at this time, it doesn't hurt to think ahead:

TYPE I ERROR: This occurs when you incorrectly reject a null hypothesis.That is, H0is true, but your sample statistic leads you to rejectH0. (You canonly make a Type I Error when H0 is true.)

TYPE II ERROR: Thisoccurs when you fail to reject a false null hypothesis. That is,H0 is false,but your sample statistics leads you to fail to rejectH0. (You canonly make a Type II Error when H0 is false.)

=======================================

Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)