課程名稱：統計導論 課程性質：選修 課程教師：江金倉 開課學院：理學院 開課系所：數學系 考試日期（年月日）：2010/11/01 考試時限（分鐘）：120 mins 是否需發放獎勵金：是 （如未明確表示，則不予發放) Introduction to Statistics (Quiz 1) 1.(12%) For each of the following situations, state which type of sampling plan was used. (1a) An airline company made a list of all its flights and randomly selected 2 flights. All of the passengers on those flights were asked to fill out a survey. (1b) A pollster divided a city into city blocks and surveyed the third house to the west southeast corner of each block. (1c) A university divided employees into tree categories: staff, faculty, and student employees. A random sample was selected from each group and they were telephoned and asked for their opinions. (1d) The store posted an interviewer at the door and told her to collect a sample of 100 opinions by asking the next person who came in the door each time she had finished an interview. 2.(16%) Distinguish between each of the following paired terms. (2a) retrospective study versus prospective study. (2b) confounding variable versus interacting variable. (2c) categorical variable versus discrete variable. (2d) case-control study versus matched-paired design. 3.(10%) Let rXY be the correlation coefficient of the sample {(X1,Y1), … , (Xn,Yn)}.Consider the re-scaled data {(U1,V1), … , (Un,Vn)} with Ui=aXi+b and Vi=cYi+d, where a and c are positive constants and b and d are any constants. Show that the correlation coefficient rUV is same with rXY. 4.(5%)(5%) Compute the mean and variance of the grouped data with f1,f2,..., fg being the frequencies of the g classes [ao,a1), [a1,a2) , ... , [ag-1,ag]. 5.(9%) Try to mark the relative positions of mean, median, and mode of bell-shaped, right skewed, and left skewed distributions, respectively. 6.(8%) Draw a box-plot via using the five-number summary: minimum=63, maximum=72, the first quartile=68, median=70, the third quartile=71. 7.(4%)(6%) In the AIDS study, let D and T denote separately the events of HIV+ patients and patients who are diagnosed as HIV+ patients. Suppose that the positive predictivity P(D|T) and the negative predictivity P(Dc|Tc) are known. What additional condition is required to compute the sensitivity P(T|D) and the specificity P(Tc|Dc)? How to compute the sensitivity and specificity? 8.(10%) To investigate the association of the smoking and lung cancer, a case-control study is conducted. Let LC and S denote separately the lung cancer patients and smokers. The conditional probabilities P(S|LC) and P(S|LCc) are known in this study. Show that the relative risk of S versus Sc can be approximated by the odds ratio of S and Sc when P(LC)≒0. 9.(7%) Consider the probability mass function f(x) of random variable X with the corresponding probabilities 0.1, 0.3, 0.1, 0.2, and 0.3 at x= 1, 2, 3, 4, and 5. Compute the probability of {1＜X≦3.5}. 10.(8%) Let A and B mutually independent events. What is the probability of A∪B? --

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