26.1	a) True (p 481)
	b) False.  The null says the difference is due to chance; the
	alternative says the effect is real.
	
26.2 	a) The test was like 3800 draws with replacement from a box 
	with an unknown number of red numbers.  The null hypothesis
	contends that the proportion of reds in the box was 18/38,
	the alternative says that the proportion of reds was greater.
	b) The expected number of reds, according to the null 
	hypothesis, is 1800 in the test.  The SE of the number of 
	reds is (3800)^.5 * .5 = 31, so the Z-score of the test is 
	about 2.9, which gives a p of about .002
	c) You can reject the null hypothesis with that p-score. 
	(note that this does not mean that you "proved" that there
	were too many reds; instead your test showed that it was 
	extremely unlikely for this number of reds to occur by chance.)
	
26.4	The TA claims that his average of 55 was the result of 30 
	draws from the box of 900 tickets with a mean of 63 and a SD
	of 20.  The SE of that draw would be 20 / (30)^.5 = 3.65, so
	the Z score for an observation of 55 would be given by:
	   (55 - 63) / 3.65 = -2.2, which has an associated p of .01.

	It is unlikely that the TA's grades are due to chance.

26.8	The data are like 1000 draws from the box of people in the 
	county.  Under the null hypothesis, the people in the county
	have the same educational background as people throughout the
	country (mean = 13 yrs, SD = 5 yrs, the spread of people in
	the sample).  The SE of the average of these draws is 
	   5 / (1000) ^.5 = .16.  z = (14-13) / .016 = 6, p about 0%.
	Some demographic factor causes this county to be more 
	educated than the nation as a whole (perhaps a college is 
	present).

26.12   a) There are 59 pairs, and in 52 of them, the treatment animal
        has a heavier cortex.  On the null hypothesis, the expected number
        is 59*0.5=29.5 and the SE is sqrt(59)*0.5=3.84.  So 52 is 
        nearly 6 SEs above average, and the chance is close to 0.
        Inference: treatment made the cortex weigh more.

        b) The average is about 36 milligrams and the SD is about 31 
        milligrams.  The SE for the average is 4 milligrams, so z=36/4=9 and
        P = about 0 (This is like the tax example in section 1).  
        Inference: treatment made the cortex weigh more.
        
        c) This binds the person doing the dissection to the treatment
        status of the animal.  It is a good idea because it prevents
        bias; otherwise the researcher might skew the results to favor
        the research hypothesis.