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課程名稱︰統計
課程性質︰必修
課程教師︰林惠玲
開課學院：社科院
開課系所︰經濟系
考試日期（年月日）︰95.4.10
考試時限（分鐘）：180
是否需發放獎勵金：是
試題 :
2006/04/10 統計學 下 第一次小考 林惠玲老師
一、 選擇題 (24%)
1. Which of the following statements is true？
(a) If we do not reject the null hypothesis based on sample evidence,
we have proven beyond doubt that the null hypothesis is true.
(b) If the null hypothesis is false and the researcher rejects it,
then a type Ⅱ error has been committed.
(c) As the alternative hypothesis mean approaches the null hypothesis mean,
we could involve a greater risk of type Ⅱ error.
(d) Non of the above statement is true.
2. Which of the following statements is true？
(a) The probability of the type Ⅰerror and the probability of
the type Ⅱ error always add to 1
(b) Increasing the value of α increasing the value of β
(c) A large value for the power at a specific value of the alternative
hypothesis indicates a small value for the probability of a type Ⅰ
error, give the specified value stated in the alternative hypothesis
(d) Non of the above statement is true
3. The null hypothesis was rejected in a hypothesis test with α=0.1.
If the p-value is 0.0071, which of the following can you conclude？
(a) We are confident about accepting
(b) We are confident about rejecting
(c) Ho is not true
(d) H1 is not true
4. Random variables X and Y are normally distributed. We know that
is not equal to , but and are sample standard deviations obtained
from samples of size 6 and 8 respectively. The is distributed as
(a) Chi-square distribution with 14 degrees of freedom.
(b) F distribution with 6 degrees of freedom in the numerator and 8
degrees of freedom in the denominator
(c) F distribution with 5 degrees of freedom in the numerator and
7degrees of freedom in the denominator
(d) Non of the above statement is true
5. Assume a two-tailed large sample hypothesis test where has been
rejected. The observed test statistic value was found to be Z=2.96.
What is the p-value？
(a) 0.4985
(b) 0.0015
(c) 0.9970
(d) 0.0030
6. What are the assumption behind the one-way ANOVA models？
(a) The observations are independent
(b) The variances are equal
(c) The observations are normally distributed.
(d) All of the above
7. Analysis of variance can be used when
(a) one is interested in determining whether or not populations have
equal variances
(b) one is interested in determining if populations are normally distributed
(c) one is interested in validating that the samples are independent
(d) one is interested in determining whether or not populations have
equal means
8. In ANOVA test, if the means of the sampled populations are equal to
each other,the ratio of will be
(a) equal to
(b) equal to 1
(c) equal to 0
(d) none of the above is true
二、
行政院主計處調查結果顯示，民國89年8月份臺灣地區製造業員工每人每月平均工作
時數為207.8小時。假設臺灣地區製造業員工每人每月的工作時數呈常態分配。（資料來
源：《薪資與生產力統計月》，行政院主計處，336期，2001年10月。）
1.
現隨機抽選25位製造業員工，調查其每月的工作時數，發現平均數為196小時，標準差
為26.5小時。當顯著水準為0.01時，製造業員工每人每月平均工作時數是否較89年8月份
少？ (6%)
2.
現隨機抽選100位製造業員工，調查其每月的工作時數，發現平均數為196小時，標準
差為26.5小時。當顯著水準為0.01時，製造業員工每人每月平均工作時數是否較89年8月
份少？ (6%)
3.
若每人每月實際平均工作時數為190小時，請分別計算1、2條件下之檢定力，並用此說
明問題1與2的結果，何者較為可信，為什麼？(8%)
t值 d.f=24 d.f=25
0.86 0.8009 0.8010
0.87 0.8035 0.8037
0.88 0.8062 0.8064
三、從兩工廠各抽取16名工人，得其每月平均工資來計算平均數和變異數如下：
__ __
Xa=21 ，Sa^2=4.5 ，Xb=19 ， Sb^2=3.9
*試檢定兩母體之變異數是否相同（alpha=0.05 ）？(6%)
*試以 及 分配檢定 與 是否相等（alpha=0.05 ）？(12%)
*你在做上面小題之檢定時，各自應有什麼樣的前提假設？(2%)
四、(14%)A political researcher believes that the fraction of KMPs strongly
in favor of the three direct links on across strait is greater than the
fraction of DPPs strongly in favor of the three direct links on across
strait. He acquired independent random samples of 200 KMPs and 200 DPPs and
found 165 KMPs and 135 DPPs strongly favoring the three direct links on
across strait. Does this evidence provide statistical support for the
researcher's belief? Use alpha=0.05.
The political researcher should have designed a test for which is
tolerably low when exceeds by a meaningful amount. For example, find a
common sample size for a test which alpha=0.05 and beta=<0.2 when, in fact,
p1 exceeds p2 by 0.2. [Hint: The maximum value of p(1-p) is 0.25.]
六、某人欲知勞保基金投入股票市場後，對各種股票的影響有多大，他搜集了下列10種股
票的資料： (10%)
1 2 3 4 5 6 7 8 9 10
前 2.3 2.0 2.1 2.4 1.9 2.2 1.8 2.4 1.6 1.7
後 2.5 1.9 2.6 2.2 2.1 2.5 2.2 2.7 1.9 1.6
差 -0.2 +0.1 -0.5 +0.2 -0.2 -0.3 -0.4 -0.3 -0.3 +0.1
若已知股價的分配為常態分配，試檢定勞保基金是否造成這一籃子股票的平均價格波動。
七、一卡片公司想以去年生日卡的銷售情形決定今年生日卡的製作方針，該公司針對四
類不同對象設計生日卡：親屬、朋友、情人、萬用卡。今隨機選取8個銷售點，其去年的
銷售記錄如下(單位：張)：
對象\銷售點 1 2 3 4 5 6 7 8
親屬(A) 164 140 152 121 165 136 146 168
朋友(B) 183 170 178 135 188 159 174 189
情人(C) 122 110 108 100 140 124 154 150
萬用卡(D) 111 96 106 88 135 97 114 109
假設各類生日卡的銷售量均呈常態分配。
1.試建立 ANOVA table 並檢定各類卡片的銷售量是否有差異(alpha=0.05 )？
並請說明此種分析模式你還需要哪些假設條件。(12%)
2.(6%)以 Bonferroni's method 檢定各類卡片平均銷售數間
是否有顯著差異(alpha=0.05 )？
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