"Algebra is generous; she often gives more than is asked of her" - (Jean Le Rond d'Alembert, 1717-1783)   George David Birkhoff (1884-1944): One of the first great American mathematicians to be recognized abroad, Birkhoff's work on dynamical systems has been used extensively by modern mathematicians and scientists. His many contributions include developing theories relating to differential equations and coloring maps. He received many worldwide honors, including the Querini-Stampalia Prize of the Royal Institute of Science,Arts and Letters of Venice in 1923. He held positions at Princeton, Harvard, and the University of Wisconsin. Why does Herkimer think that coffee gets its name from a famous childrens' story? Answer: He thought it was Snow White's eighth dwarf, the first cousin of Sneezy. Herky wants to know: Should you volunteer for submarine duty if you don't want to get on a ship that sinks on purpose? Is it true that those who exercise regularly die healthier? ASSIGNMENT #73 Reading:. Review Section 11.2, as necessary. Exercises:11.37, 11.38, 11.39 (page 631) Write these up as you would for an AP essay.

You are working in section 11.2.

What is below is mostly a repeat fromassignment #72. It is important.

The two-sample t statistic for difference of meansis

t = [(x1-x2)-(m1-m2)]/sqrt(s12/n1 + s22/n2)

degrees of freedom is the smaller ofn1-1,n2-1.

The denominator of this statistic is based on thefact that "variances add." (Check Rules for Variances on page 400.)This is illustrated in the simple example below. In thisillustration, the set x1 + x2 is formed by adding pairs ofelements, 5+2, 5+4, 9+2, 9+4, 13+2, 13+4. The set x1-x2 is formed by subtractingpairs of elements, 5-2, 5-4, 9-2, 9-4, 13-2, 13-4. Note (and we arespeaking somewhat loosely here)...

• Variances add, but don't subtract.
• Standard deviations do not add.

 x1 x2 x1+ x2 x1- x2 5 2 7 3 9 4 9 1 13 11 7 13 5 15 11 17 9 Means 9 3 12 6 Means and and subtract [9+3 = 12, 9-3 = 6] Standard Deviations 3.2660 1 3.4157 3.4157 Standard deviations do not add or subtract. [3.2660+1 is not 3.4157] Variances 10.6667 1 11.6667 11.6667 Variances add only [10.6667 + 1 = 11.6677]

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

Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (;l 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)