課程名稱︰統計導論
課程性質︰數學系選修
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）︰2016.11.2
考試時限（分鐘）：50
試題 :
Introduction to Statistics (Test 2)
1.(30%) State or explain the following terms.
(1a) stratified random sampling. (1b) case-control study.
(1c) retrospective study. (1d) confounding variable.
(1e) Hawthorne effect. (1f) five number summary.
2.(10%) Draw a box-plot via using the five number summary: minimum=63,
maximum=72, the first quartile=68, median=70, the third quartile=71.
3. Let X be the scores of an entrance examination with mean 60 and standard
deviation 5.
(3a)(5%) Define the corresponding Z-score of X variable.
(3b)(5%) What is the original score of Z=2?
4.(10%) Compute the coefficient of variation of the grouped data with f_1,f_2,
...,f_g being the frequencies of the g classes [a_0,a_1), [a_1,a_2),...,
[a_(g-1),a_g].
5.(10%) A case control study in Berlin asked 239 lung cancer patients and 429
controls (matched to the cases by age and sex) whether they kept a pet bird
during adulthood. Of the 239 lung cancer cases, 98 said yes. Of the 429
controls, 101 said yes. Construct a contingency table for the data.
6. Let r_XY be the correlation coefficient of the sample {(X_1,Y_1),...,
(X_n,Y_n)}.
(6a)(7%) Compute the sample correlation coefficient r_XY of X and Y variables.
(6b)(2%)(2%)(2%) Explain the meanings of r_XY=1, r_XY=-1, and r_XY=0,
respectively.
(6c)(7%) For the re-scaled data {(U_1,V_1),...,(U_n,V_n)} with U_i=a(X_i)+b
and V_i=c(Y_i)+d, where a and c are positive constants and b and d are any
constants, let r_UV stand for the sample correlation coefficient of U and V
Variables. Find the relation between r_UV and r_XY.
(6d)(10%) Compout r_XY for Y_i=β_0+β_1(X_i), i=1,...,n, where β_1>0.