課程名稱︰初級統計學下
課程教師︰張宏浩
開課學院：管理學院
開課系所︰會計系
考試日期（年月日）︰2010年6月22日
考試時限（分鐘）：13:20-16:10
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(10%)Four-o'clock, Mirabilis jalapa, are plants native to tropical America.
Individual four-o'clock plants can have red, white or pink flowers. According
to Mendelian genetic principles, self-pollination of pink-flowered plants
should produce progeny that have red, pink and white flowers in a 1:2:1 ratio.
A scientist self-pollinates several pink-flowered plants and produces 240
progeny with 55 that are red-flowered, 132 that are pink-flowered and 53 that
are white-flowered. Are these data reasonably consistent with the m=Mendelian
model?(α=0.05)
2.(10%)Wang Corporation is interested in determining whether a relationship
exists between the commuting time of its employees and the level of stress-
related problems observed on the job. A study of 123 assembly-line workers
reveal the following:
Commuting time High Moderate Low Total
Under 15 min 10 6 19 35
15-45min 15 9 29 53
Over 45 min 20 7 8 35
Total 45 22 56 123
At the 0.01 level of significance, is there evidence of a significant
relationship between commuting time and stress level?
(Note:you are required to specifically indicate your null and alternative
hypotheses)
3.(15%)A marketing analyst for a shoe manufacturer is considering the
development of a new brand of walking shoes. The marketing analyst wants to
determine which variables to use in predicting durability. Two independent
variables under consideration are X1(FOREIMP), a measurement of the forefoot
shock-absorbing capability, and X2(MIDSOLE), a measurement of the change in
impact properties over time. The dependent variable Y is LTIMP, a measurement
of the shoe's durability after a repeated impact test. A random sample of 21
types of currently manufactured walking shoes was selected for testing, with
the following incomplete results:
Table 1
Variable Coefficients Standard Error t statistics
Intercept -0.02686 0.06905 (a)
FOREIMP 0.79116 0.02695 NA
MIDSOLE 0.60484 0.07174 NA
Table 2
Source Degree of Freedom Sum of Squares
Regression 2 90
Error 18 130
Total 20 220
<PS>SSR(X1)=45, SSR(X2)=25, α=0.05
(1)(5%)Please caculate (a) in Table 1, and specify what is the definition of
t statistics in table in. (with its null and alternative hypotheses)
(2)(5%)Please use Table 2 to decide whether there is a significant
relationship between LTIMP and FOREIMP (note: assume you do not have table 1,
so you are forbidden to use information from table 1 to answer this question.)
(3)(5%)Please compute the coefficients of partial determination of MIDSOLE,
and interpret their meaning.
4.下表為A公司5種營養補給品與B公司6種營養補給品每100克之蛋白質含量(單位:克)
A公司 B公司
5.03 4.5
5.36 3.7
5.24 5.0
5.23 4.0
5.69 4.9
5.7
檢定A公司產品與B公司產品每百克之蛋白質含量之中位數是否有顯著性差異(顯著水準
為0.05)。
(1)(7%)使用Wilcoxon Rank Sum 檢定法。
(α=0.05, n1=5, n2=6, (WL,WU)=(19,41))
(2)(8%)使用Mann-Whitney 檢定法。
(n1=5, n2=6, P(U≦5)=0.041)
5.(10%)「安栗」、「如薪」兩競爭的直銷公司旗下銷售員去年業績如下:(單位:萬元)
安栗 如薪
2.8 3.3
3.1 2.7
2.7 3.5
2.5 3.0
2.9 3.8
3.5 2.8
3.9 3.0
3.3 3.4
3.2 4.1
4.3 4.2
3.7 4.4
3.6
4.0
2.7
由於此屬於大樣本，在顯著水準0.05下，Mann-Whitney檢定法可近似常態分配，試以此
常態分配檢定兩直銷公司銷售元之業績中位數是否有顯著性差異?
6.(10%)摳思凍、哈跟答思、肚老爺三個品牌不同冰淇淋之熱量如下:(單位:kcal)
摳思凍 哈跟答思 肚老爺
70 72 70
82 80 70
54 83 52
在顯著水準0.05下，試以Kruskal-Wallis Rank Test 檢定三種品牌所出冰淇淋熱量中位
數是否有顯著性差異。
7.(15%)Assume y, x1 and x2 represent the production yield, and capital uses of
rice production in Taiwan. A regression model is set up as below:
log(yi)=α+β1×log(x1i)+β2×log(x2i)+εi
(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.
8.(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 regression 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.
9.(10%)Given the sample of a series observation of (yi,xi), is there any
possibility to examine whether the effects of xi on yi is a second-order
non-linear relationship? How to set up the regression model and how to
estimated coefficients.
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