2.3 An archaeologist numbers some articles 1 to 11 in the order he discovers the
ID: 3068274 • Letter: 2
Question
2.3 An archaeologist numbers some articles 1 to 11 in the order he discovers them. He selects at random a sample of 3 of them. What is the probability that the sum of the numbers on the items he selects is less than or equal to 8? (You do not need to list all combinations of 3 items from 11 to answer this question.) If the archaeologist believed that items belonging to the more recent of two civ- ilizations were more likely to be found earlier in his dig and of his 11 items 3 are identified as belonging to that more recent civilization (but the remaining 8 come from an earlier civilization) does a rank sum of 8 for the 3 matching the more recent civilization provide reasonable support for his theory? 2.4 A library has on its shelves 114 books on statistics. I take a random sample of 12 and want to test the hypothesis that the median number of pages, , in all 114 books is 225. In the sample of 12, note that 3 have less than 225 pages. Does this justify retention of the hypothesis that 225? what should I take as an appropriate alternative hypothesis? What is the largest critical region for a test with P 0.05 and what is the corresponding exact P-level? 2.5 The numbers of pages in the sample of 12 books in Exercise 2.4 were: 126 142 156 228 245 246 370 419 433 454 478 503 Find a confidence interval at a level not less than 95 percent for the medianExplanation / Answer
2.5 we know that the confidence interval of quantiles is given as
j = nq - 1.96 root(nq(1-q))
k = nq + 1.96 root(nq(1-q))
where q is the quantile which in this case would be 0.5 (median) , median is 308 as the number of pages is even - 12
n is median which would be 308
putting the values we get
j = 308*0.5 - 1.96 root(308*0.5(1-0.5))
k = 308*0.5 -+1.96 root(308*0.5(1-0.5))
136.80 and 171.19
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