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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