"The universe stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures." - (Galileo, 1564-1642)   Luitzen Brouwer (1881-1966: A Dutch mathematician, Brouwer was the leader of the intuitionist mathematicians. The intuitionists believe mathematics is a human activity that originates and thrives in the mind, and that it is independent of the real world. They believe that a logical construction of the system of the real numbers is not acceptable. Their views conflicted with those of the formalist mathematicians led by David Hilbert, and the logistic school of mathematicians led by Alfred North Whitehead and Bertrand Russell. Why wouldn't Herkimer let a friend pull a wagonload of sheep over his tray of ice cubes? Answer: He didn't want anyone pulling the wool over his ice. Herky wants to know: Why do those who claim to live by their wits always look so hungry? Do those who have a desperate urge to paint themselves gold have a gilt complex? ASSIGNMENT #72 Reading: Read the following very carefully. STAT PACK handout (pages 14C,14d). Cartoon Guide to Statistics, pages 168-169. Main Text (YMM) Section 11.2, pages 617-627. Exercises: None, study the examples presented in the readings.

You are working in section 11.2.

The two-sample t statistic for difference of meansis

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

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 setx1-x2 is formed by subtracting pairs of elements, 5-2, 5-4, 9-2,9-4, 13-2, 13-4. Note (and we are speaking somewhat looselyhere)...

• 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]

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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)