"Courage lies in the wanting to know, which solves nothing, but which has within itself all solutions." -- (Francoise Mallet-Joris) Numbers have interesting historical backgrounds, and there are many interesting stories behind just about any counting number. Here are just a few very brief tidbits relating to numbers. Some research will yield many interesting stories. Previous Tidbits have referenced the digits 1,2,3,4,5,6,7,8,9, and a few other numbers. Here are brief statements about some other numbers. 108: Tibetan sacred scriptures, the Tanjur and the Kanjur, contain 108 parts. 120: This number is connected with lifespan in Old Testament (Genesis 6:3) 153: The disciples of Christ catch exactly 153 fishes (John 21:11) 248: This number has a prominent place in Judaism as it represents the numerical value of the first two words of the fundamental religious expression of monotheism, "Hear, O Israel." 666: The number of the Beast (Revelation 13:8) in the Christian Bible. What did Herkimer say to the noisy people who lived in the apartment below his? Answer: Do under others as you would have them do under you. Herky's words of wisdom: Read contracts carefully. The fine print may be a clause for suspicion. Make sure your dentist is honest. When he does an extraction, you should make sure you get the tooth, the whole tooth, and nothing but the tooth. ASSIGNMENT #62 Reading: Section 10.2, pages 540-548. Exercises: 10.39, 10.40 (page 549). Write these up neatly on a separate piece of paper. (Communicate as you would on the actual AP Examination.

You are working in Section 10.2.

Example:

A particular brand of tire has a mean lifem =36,000 miles and a standard deviation s = 3,000 miles. A change in themanufacturing process makes the manufacturer think that the mean lifehas been increased. A random sample of 130 tires produces a mean lifeof 36,600 miles. Is there reason to believethat the manufacturing process change has increased the mean life ofthe tires?

• Null hypothesis H0: m = 36,000
• Alternate hypothesis Ha: m > 36,000

Consider the collection of sample means x(bar)form samples of size 130. The Central Limit Theorem tells us that ifH0 is true,then

mx(bar) = 36,000 andsx(bar) = 3,000/sqrt(130) =263.12.

How likely is a random sample of 130 with mean =36,600? The P-value is normalcdf(36600,1E99,36000,263.12) = .0113, or 1.13%.In other words, if H0 is true, there is about a 1.13% probability of obtaining asample with mean = 36,600 miles. The statistics 36,600 is significantat the 5% level, but it is not statistically significant at the 1%level. In formal statistical terms, we reject H0 and the 5% level ofsignificance, and we fail to reject H0 at the 1% level ofsignificance.

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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)