| 一、 選擇題（5題，每題2分，共10分） |
| 1. |
Since the population size is always larger than the sample
size, then the sample statistic |
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a. can never be larger than the population parameter
b. can never be equal to the population parameter
c. can never be zero
d. can never be smaller than the population parameter
e. None of the above answers is correct.
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| 2. |
A nonparametric version of the Parametric analysis of variance
test is the |
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a. Kruskal-Wallis Test
b. Mann-Whitney-Wilcoxon Test
c. sign test
d. Wilcoxon signed-rank test
e. None of the above answers is correct.
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| 3. |
An important application of the chi-square distribution
is |
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a. when making inferences about a single population variance
b. when testing for goodness of fit
c. when testing for the independence of two variables
d. All of the above answers are correct.
e. None of the above answers are correct.
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| 4. |
Regression analysis is a statistical procedure for developing
a mathematical equation that describes how |
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a. one independent and one or more dependent variables are related
b. several independent and several dependent variables are related
c. one dependent and one or more independent variables are related
d. All of the above answers are correct.
e. None of the above answers is correct.
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| 5. |
To avoid the problem of not having access to Tables of F
distribution with values given for the lower tail, the numerator of the
test statistic should be the one with |
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a. the larger sample size
b. the smaller sample size
c. the larger sample variance
d. the smaller sample variance
e. None of the above answers is correct.
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| 二、 填充題（10格，每格4分，共40分） |
| 1. |
事件A1, A2和A3的先驗機率分別為P(A1)
= 0.20, P(A2) = 0.50, P(A3) = 0.30。條件機率 P(B∣A1)
= 0.50, P(B∣A2) = 0.40, P(B∣A3) = 0.30。在此想請問事後機率
P(A2∣B) = j 。 |
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| 2. |
某公司辦公室的電話鈴聲響起時間（分鐘）呈下列指數分配：f(x) = 0.5 e -0.5x
, x≧0 ，請問下一個鈴聲在30秒內會響起的機率是多少? k （請寫出算式即可）。如果有另外一個辦公室的電話鈴聲頻率為每2分鐘1通電話，請問5分鐘內打入3通的機率是多少? l （請寫出算式即可）。 |
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| 3. |
某產品若抽樣100件有5%以上的不良品的話則不能交貨，如果已知不良品的母體比例 r＝0.1，問
會大於0.05的機率是多少? m 。 |
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| 4. |
某公司員工年齡的資料分佈如下，請計算其變異係數 n 。 |
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年齡
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30-39
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40-49
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50-59
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60-69
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70-79
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次數(人)
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2
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3
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7
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5
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1
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| 5. |
在某項調查中，母體比例 r之計畫值被設為0.35，那麼需要有多大的樣本數才能使在95%的信賴水準下抽樣誤差在
±0.05內? o 。（計算過程中請勿四捨五入） |
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| 6. |
某蛋糕店宣稱其每個蛋糕中至少含有9片的巧克力脆片。為了檢驗其宣稱是否屬實，我們進行抽樣，結果平均每個蛋糕含有7.875片的巧克力脆片，標準差為1。當我們以a
= 0.01的顯著水準來進行檢定，如果每個蛋糕含有巧克力脆片的真實數字為8，請問我們犯型II誤差的機率是多少? p 。 |
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| 7. |
考慮下列假設檢定：H0:m1－m2=0;
Ha: m1－m2≠0，下表為取自兩母體的獨立樣本結果。當a
= 0.05時，其 r值為何? q 。 |
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樣本1
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n1=80
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=104 |
s1=8.4
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樣本2
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n2=70
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 =106 |
s2=7.6
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| 8. |
一個迴歸模型有46個觀察值，其估計迴歸方程式如下： |
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 ＝
17＋4X1-3X2＋8X3＋5X4＋8X5 |
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已知此模型的SST＝3410, SSE＝510，請問透過ANOVA table計算出來的F值為何? r 。 |
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| 9. |
包含30組觀察值的迴歸分析，建立了如下的估計迴歸方程式： ＝
17.6＋3.8X1-2.3X2＋7.6X3＋2.7X4，已知SST＝1805,
SSR＝1760。假如在模型中刪去自變數X1與X4，得到新的估計迴歸方程式 ＝ 11.1-3.6X2＋8.1X3，且其SST＝1805,
SSR＝1705。當我們想在a = 0.05的情況下，用F檢定來判斷X1與X4對模型的貢獻是否顯著時，其所計算出來的F值為何? s 。 |
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| 三、 計算題（4題，共50分） |
| 1. |
You are given the following results from a sample of 5 observations. |
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4 6 3 4 3 |
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a. |
Construct a 99% confidence interval for the population variance. (3分) |
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b. |
The null and alternative hypotheses are H0: σ2≧ 2 and Ha:σ2＜ 2,
Compute the test statistic. (3分) |
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c. |
Perform the test of the hypothesis at the 1% level, what do you conclude
about the population variance? (4分) |
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| 2. |
A manufacturing company designed a factorial experiment
to determine whether the number of defective parts produced by two machines
differed and if the number of defective parts produced also depended on
whether raw material needed by each machine was loaded manually or by
an automatic feed system. The following data give the numbers of defective
parts produced. Using a = 0.05, test for any
significant effect due to machine, loading system, and interaction. (15分) |
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Loading System
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Manual
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Automatic
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Machine 1
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30
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30
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34
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26
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Machine 2
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20
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24
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22
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28
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| 3. |
Given are five observations collected in a regression study
on two variables. |
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Xi
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2
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4
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5
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7
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8
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Yi
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2
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3
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2
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6
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4
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a. |
Develop the estimated regression equation for these data. (5分) |
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b. |
What is the value of the standard error of the estimate? (5分) |
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c. |
Test for a significant relationship by using the test. Use a
= 0.05. (5分) |
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| 4. |
It is believed that the median age of
college students is 21 years. A sample of 80 college students is taken.
Thirty of the students were under 21, 45 of the students were over 21,
and 10 were 21 years old. |
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a. |
State the null and alternative hypotheses. (3分) |
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b. |
Test the null hypothesis at the 1% level of significance. (7分) |
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| t分配表 |
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| Z分配表 |
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