課程名稱︰統計學
課程性質︰必修
課程教師︰張宏浩
開課學院：
開課系所︰農經系
考試日期（年月日）︰09.06.10
考試時限（分鐘）：3hr 2:00-5:00
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(15%)The following data are the monthly salaries y and the grade point
averages x for students who obtained a bachelor's degree in business
administration with a major in information systems. The estimated
regression equation for the data is
^
y = 1790.5 + 581.1x
GPA 2.6 3.4 3.6 3.2 3.5 2.9
Monthly
Salary 3300 3600 4000 3500 3900 3600
($)
(1)Compute SST, SSR and SSE.
(2)Compute the coefficient of determination R^2. Comment on the goodness
of the fit and explain the meanings of R^2 by words.
(3)What is the value of the sample correlation coefficient?
2.(20%)In a manufacturing process the assembly line speed (feet per minute)
was thought to affect the number of defective parts found during the
inspection process. To test this theory, managers devised a situation in
which the same batch of parts was inspected visually at a variety of line
speeds. They collected the following data.
Line Speed 20 20 40 30 60 40
Number of
Defective 21 19 15 16 14 17
Parts
(1)Develop the estimated regression equation that relates line speed to
the number of effective parts found.
(2)At a 0.05 level of significance, determine whether line speed and the
number of defective parts found are related.(6%)
(3)Did the estimated regression equation provide a good fit to the data?
(4)Develop a 95% confidence interval to predict the mean number of
defective parts for a line speed of 50 feet per minute.
3.(10%)某公司宣稱所產生的電池負載載量至少為140安培小時。一消費者保護基金會
想檢定此公司的宣稱是否可信，於是隨機抽樣20個個樣本，並檢測其負載量，所得
結果如下:
137.0 140.0 138.3 139.0 144.3 139.1 141.7 137.3 133.5 138.2
141.1 139.2 136.5 136.5 135.6 138.0 140.9 140.6 136.3 134.1
試檢定此公司之宣稱是否屬實? 請以Wilcoxon-Sign Rank Test檢定之
4.(20%)一香菸製造商宣稱其新品牌香菸的焦油成分為17毫克。隨機抽取24之為樣本，
所得結果如下；
16.9 16.6 17.3 17.5 17.0 17.2 16.1 16.4 17.3 15.9 17.7 18.3
15.6 16.8 17.1 17.2 16.4 18.1 17.4 16.7 16.9 16.0 16.5 17.8
是否有證據顯示此一牌的香菸之焦油成分的中位數不為17毫克? 請分別以Wilcoxon-
Sign Rank Test 以及 Mann-Whiteney Test 檢定之，並比較其統計結論是否相同?
5.(15%)The average temperatures (度C) for a 12-month period in Taipei(X1)
and Kaohsiung(X2) are collected as below.
Taipei 16 16 18 22 25 28 29 29 27 24 21 18
Kaohsiung 19 20 22 25 27 28 29 28 28 26 23 20
Base on these samples and assume variances are equal. At the 0.05 level
of significant, please use 3 different testing methods to conclude whether
there is any evidence to show the weather differs between Taipei and
Kaohsiung?
12 12 12 12
ΣXi1 = 273, ΣXi2 = 295, ΣXi1^2 = 6481, ΣXi2^2 = 7397
i=1 i=1 i=1 i=1
t(0.05,22)=1.7171, t(0.05,24)=1.7109, t(0.025,22)=2.0739
t(0.025,24)=2.0639, t(0.1563,22)=1.0337
(a)Use Independent T-test method with critical value. 考試時助教說
(b)Use p-value method and write out the exactly p-value.←不用寫(沒表)
(c)Use 100(1-α)% Confidence Interval method and find out the confidence
interval of μ1-μ2.
Notice: White down the hypothesis and the conclusion for each testing method!
6.Assume y, x1 and x2 represent the production yield, labor, and capital used
of rice production in Taiwan. A regression model is set up as below:
㏒(yi) = α+β1㏒(X1i)+β2㏒(X2i)+ε
(a)Explain the economic meanings of the parameters β1 and β2?
(b)How to conduct the test to see if the rice production technology is
constant return to scale? Please write down the step carefully and
the associated formula of the test.
7.(15%)Assume a researcher would like to examine the effects of education
levels on wage. If the education levels are categorical and there are
three categories defined in the sample (college, high school, less than
high school).
(a)How to set up a regresstion model to analyze this problem?
(b)How to explain the meanings of parameters associated with the
education levels?
(c)How to test if the returns of college education is double than the
returns of those didn't finish high school? Please write down the
necessary hypotheses and test procedure associated with your model.
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