Section6.2posted

Section6.2posted - STOR155,Section2 Thursday,April8,2010...

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STOR 155, Section 2 Thursday, April 8, 2010 Section 6.2
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Suppose 100 tosses of a coin produce 64 heads and  36 tails.  Is this compatible with the hypothesis that the  coin is fair? How we answer this statistically: With a fair coin , the mean number of heads in 100 tosses  is 50.  We observed a deviation of 14 from this. The probability of such a deviation (14 or more away from  50)  with a fair coin  is 0.0052.  (How to get this?  Section  5.1.)  So there are just two possibilities: Either   the coin is fair and we have observed something whose  probability is only 0.0052, Or  the coin is not fair. Since 0.0052 is so small, we are inclined to decide that the  coin is not fair. 6.2 Tests of significance:  The basic  reasoning Example 1
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test of significance  starts with hypothesis  about a parameter and data   which may seem to deviate from what we would expect if the  hypothesis were true, and asks the question:  Are the data  compatible  with the hypothesis, or do the data  support  rejecting  the hypothesis in favor of some alternative  hypothesis? In Example 1 above, and in Chapter 8, the parameter is  p , the probability of heads the hypothesis to be tested is:   p = p 0    (  = ½   in Example 1) the alternative hypothesis is:   p ≠ p 0 the data are:  the count of successes in  n  trials (64 out of 100 in  Example 1)   In the rest of Section 6.2, and in Chapter 7, the parameter is  µ , the mean of a population the hypothesis to be tested is:  µ = µ 0   (some hypothesized value) the alternative hypothesis may be  µ ≠ µ 0    or  µ > µ 0    or  µ < µ 0   the data consist of a SRS and its mean  x 6.2 Tests of significance:  The basic  reasoning _
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hypotheses The hypothesis to be tested is called the  null hypothesis  and denoted  H 0 .     (“H-zero” or “ H- nought”) The  alternative hypothesis   is denoted  H a .   It is what we think is true if the null  hypothesis is false. Typically we suspect that 
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Section6.2posted - STOR155,Section2 Thursday,April8,2010...

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