Question

Problem 1. Consider the two data collections (x,..-, X) and (y,. ya). The median difference statistic is the median of the (v-x) differences for the mn possible (x, y.) pairings, i= 1, ..., mandj = 1, . . ., n. Construct two specific data collections (x,. Xm) and (y,. .. V) that demonstrate that the median difference statistic is not equal to the difference in the separate medians for the two collections Problem 2. A Venn diagram is a graphical display where the sample space S is represented by a rectangular region and events are denoted by elliptical or circular subsets of the rectangular region. Create a Venn diagram for two events A and B that are not disjoint. Identify the events A n B, and A n B on your diagram. Problem 3. Suppose that Z has a standard normal distribution. Find the following probabilities: (a) P(Z< 1.5); (b) P(Z> 1.5); (c) P(O < Z < 1.5); (d) P(-1.5<Z< 1.5). Note that R suggests: >pnorm(1.5) [1] 0.9331928 Problem 4. Let p be the probability of the event A in a population. Suppose that A occurs in 30 out of 50 observations from the population. (a) Compute an approximate 92% confidence interval for p. (b) What approximate confidence do you have in the interval obtained in part (a) if the sample size had been 100 (with 60 event A occurrences) instead of 50? (c) Discuss your findings in parts (a)-(b). >qnorm(1-.92/2) [1] 0.1004337 qnorm (. 92) [1] 1.405072 qnorm (1-.08) [1] 1.4050 72 >qnorm (1-.92) [1] -1.405072 >pnorm (2.475844) [1] 0.9933539 > qnorm (1-.08/2) [1) 1.750686

Answer 1

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